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Riemann Zeta Zero Sum

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Riemann Zeta

Riemann Zeta [Pdf/ePub] eBook Author: ,
Editor: iUniverse
ISBN-10: 9781462060368
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Riemann Zeta by , Book Summary:

You don’t know what it is to be me—the drug that I am, the drug I will be, the pure ecstasy. Here, let me cook up some of me! The world is not as it seems. But forget the world for now... The City stands alone as the only haven from government oppression, intentionally left so to serve mankind through its technological advances. The price this paradise pays for its creative freedom is deeper in cost than its denizens could ever fathom. The driver has been assigned a position at Civil Central Command, a relatively simple commission in a city with few regulations. However, this job requires much more work to investigate numerous unexplained deaths. People are dying—everywhere. With hardly any trail to go on, the driver is chasing a wraith. The City’s light of advancement is darkened by death and destruction as two travelers set upon the City and square off in a showdown. The killer is restless... How many more must litter the floor?

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Limit Theorems for the Riemann Zeta-Function

Limit Theorems for the Riemann Zeta-Function [Pdf/ePub] eBook Author: Antanas Laurincikas
Editor: Springer Science & Business Media
ISBN-10: 9401720916
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Limit Theorems for the Riemann Zeta-Function by Antanas Laurincikas Book Summary:

The subject of this book is probabilistic number theory. In a wide sense probabilistic number theory is part of the analytic number theory, where the methods and ideas of probability theory are used to study the distribution of values of arithmetic objects. This is usually complicated, as it is difficult to say anything about their concrete values. This is why the following problem is usually investigated: given some set, how often do values of an arithmetic object get into this set? It turns out that this frequency follows strict mathematical laws. Here we discover an analogy with quantum mechanics where it is impossible to describe the chaotic behaviour of one particle, but that large numbers of particles obey statistical laws. The objects of investigation of this book are Dirichlet series, and, as the title shows, the main attention is devoted to the Riemann zeta-function. In studying the distribution of values of Dirichlet series the weak convergence of probability measures on different spaces (one of the principle asymptotic probability theory methods) is used. The application of this method was launched by H. Bohr in the third decade of this century and it was implemented in his works together with B. Jessen. Further development of this idea was made in the papers of B. Jessen and A. Wintner, V. Borchsenius and B.

Download or read Limit Theorems for the Riemann Zeta-Function book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). The subject of this book is probabilistic number theory. In a wide sense probabilistic number theory is part of the analytic number theory, where the methods and ideas of probability theory are used to study the distribution of values of arithmetic objects. This is usually complicated, as it is difficult to say anything about their concrete values. This is why the following problem is usually investigated: given some set, how often do values of an arithmetic object get into this set? It turns out that this frequency follows strict mathematical laws. Here we discover an analogy with quantum mechanics where it is impossible to describe the chaotic behaviour of one particle, but that large numbers of particles obey statistical laws. The objects of investigation of this book are Dirichlet series, and, as the title shows, the main attention is devoted to the Riemann zeta-function. In studying the distribution of values of Dirichlet series the weak convergence of probability measures on different spaces (one of the principle asymptotic probability theory methods) is used. The application of this method was launched by H. Bohr in the third decade of this century and it was implemented in his works together with B. Jessen. Further development of this idea was made in the papers of B. Jessen and A. Wintner, V. Borchsenius and B.


The Riemann Hypothesis

The Riemann Hypothesis [Pdf/ePub] eBook Author: Peter Borwein,Stephen Choi,Brendan Rooney,Andrea Weirathmueller
Editor: Springer Science & Business Media
ISBN-10: 0387721266
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The Riemann Hypothesis by Peter Borwein,Stephen Choi,Brendan Rooney,Andrea Weirathmueller Book Summary:

This book presents the Riemann Hypothesis, connected problems, and a taste of the body of theory developed towards its solution. It is targeted at the educated non-expert. Almost all the material is accessible to any senior mathematics student, and much is accessible to anyone with some university mathematics. The appendices include a selection of original papers that encompass the most important milestones in the evolution of theory connected to the Riemann Hypothesis. The appendices also include some authoritative expository papers. These are the “expert witnesses” whose insight into this field is both invaluable and irreplaceable.

Download or read The Riemann Hypothesis book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). This book presents the Riemann Hypothesis, connected problems, and a taste of the body of theory developed towards its solution. It is targeted at the educated non-expert. Almost all the material is accessible to any senior mathematics student, and much is accessible to anyone with some university mathematics. The appendices include a selection of original papers that encompass the most important milestones in the evolution of theory connected to the Riemann Hypothesis. The appendices also include some authoritative expository papers. These are the “expert witnesses” whose insight into this field is both invaluable and irreplaceable.


The Riemann Zeta-Function

The Riemann Zeta-Function [Pdf/ePub] eBook Author: Aleksandar Ivic
Editor: Courier Corporation
ISBN-10: 0486140040
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The Riemann Zeta-Function by Aleksandar Ivic Book Summary:

This text covers exponential integrals and sums, 4th power moment, zero-free region, mean value estimates over short intervals, higher power moments, omega results, zeros on the critical line, zero-density estimates, and more. 1985 edition.

Download or read The Riemann Zeta-Function book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). This text covers exponential integrals and sums, 4th power moment, zero-free region, mean value estimates over short intervals, higher power moments, omega results, zeros on the critical line, zero-density estimates, and more. 1985 edition.


The Riemann Zeta-Function

The Riemann Zeta-Function [Pdf/ePub] eBook Author: Anatoly A. Karatsuba,S. M. Voronin
Editor: Walter de Gruyter
ISBN-10: 3110886146
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The Riemann Zeta-Function by Anatoly A. Karatsuba,S. M. Voronin Book Summary:

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Download or read The Riemann Zeta-Function book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany


Multiplicative Number Theory

Multiplicative Number Theory [Pdf/ePub] eBook Author: H. Davenport
Editor: Springer Science & Business Media
ISBN-10: 1475759274
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Multiplicative Number Theory by H. Davenport Book Summary:

Although it was in print for a short time only, the original edition of Multiplicative Number Theory had a major impact on research and on young mathematicians. By giving a connected account of the large sieve and Bombieri's theorem, Professor Davenport made accessible an important body of new discoveries. With this stimula tion, such great progress was made that our current understanding of these topics extends well beyond what was known in 1966. As the main results can now be proved much more easily. I made the radical decision to rewrite §§23-29 completely for the second edition. In making these alterations I have tried to preserve the tone and spirit of the original. Rather than derive Bombieri's theorem from a zero density estimate tor L timctions, as Davenport did, I have chosen to present Vaughan'S elementary proof of Bombieri's theorem. This approach depends on Vaughan's simplified version of Vinogradov's method for estimating sums over prime numbers (see §24). Vinogradov devised his method in order to estimate the sum LPH e(prx); to maintain the historical perspective I have inserted (in §§25, 26) a discussion of this exponential sum and its application to sums of primes, before turning to the large sieve and Bombieri's theorem. Before Professor Davenport's untimely death in 1969, several mathematicians had suggested small improvements which might be made in Multiplicative Number Theory, should it ever be reprinted.

Download or read Multiplicative Number Theory book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). Although it was in print for a short time only, the original edition of Multiplicative Number Theory had a major impact on research and on young mathematicians. By giving a connected account of the large sieve and Bombieri's theorem, Professor Davenport made accessible an important body of new discoveries. With this stimula tion, such great progress was made that our current understanding of these topics extends well beyond what was known in 1966. As the main results can now be proved much more easily. I made the radical decision to rewrite §§23-29 completely for the second edition. In making these alterations I have tried to preserve the tone and spirit of the original. Rather than derive Bombieri's theorem from a zero density estimate tor L timctions, as Davenport did, I have chosen to present Vaughan'S elementary proof of Bombieri's theorem. This approach depends on Vaughan's simplified version of Vinogradov's method for estimating sums over prime numbers (see §24). Vinogradov devised his method in order to estimate the sum LPH e(prx); to maintain the historical perspective I have inserted (in §§25, 26) a discussion of this exponential sum and its application to sums of primes, before turning to the large sieve and Bombieri's theorem. Before Professor Davenport's untimely death in 1969, several mathematicians had suggested small improvements which might be made in Multiplicative Number Theory, should it ever be reprinted.


Zero Sum Game

Zero Sum Game [Pdf/ePub] eBook Author: S. L. Huang
Editor: Tor Books
ISBN-10: 1250180260
Size: 1870 kb
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Zero Sum Game by S. L. Huang Book Summary:

ZERO SUM GAME Best of Lists: * Best Books of the Month at The Verge, Book Riot, Unbound Worlds, SYFY, & Kirkus * The Mary Sue Book Club Pick * Library Journal Best Debuts of Fall and Winter A blockbuster, near-future science fiction thriller, S.L. Huang's Zero Sum Game introduces a math-genius mercenary who finds herself being manipulated by someone possessing unimaginable power... Cas Russell is good at math. Scary good. The vector calculus blazing through her head lets her smash through armed men twice her size and dodge every bullet in a gunfight, and she'll take any job for the right price. As far as Cas knows, she’s the only person around with a superpower...until she discovers someone with a power even more dangerous than her own. Someone who can reach directly into people’s minds and twist their brains into Moebius strips. Someone intent on becoming the world’s puppet master. Cas should run, like she usually does, but for once she's involved. There’s only one problem... She doesn’t know which of her thoughts are her own anymore. "Fresh and exciting... a great start to an exciting series--and an exciting career." --Boing Boing At the Publisher's request, this title is being sold without Digital Rights Management Software (DRM) applied.

Download or read Zero Sum Game book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). ZERO SUM GAME Best of Lists: * Best Books of the Month at The Verge, Book Riot, Unbound Worlds, SYFY, & Kirkus * The Mary Sue Book Club Pick * Library Journal Best Debuts of Fall and Winter A blockbuster, near-future science fiction thriller, S.L. Huang's Zero Sum Game introduces a math-genius mercenary who finds herself being manipulated by someone possessing unimaginable power... Cas Russell is good at math. Scary good. The vector calculus blazing through her head lets her smash through armed men twice her size and dodge every bullet in a gunfight, and she'll take any job for the right price. As far as Cas knows, she’s the only person around with a superpower...until she discovers someone with a power even more dangerous than her own. Someone who can reach directly into people’s minds and twist their brains into Moebius strips. Someone intent on becoming the world’s puppet master. Cas should run, like she usually does, but for once she's involved. There’s only one problem... She doesn’t know which of her thoughts are her own anymore. "Fresh and exciting... a great start to an exciting series--and an exciting career." --Boing Boing At the Publisher's request, this title is being sold without Digital Rights Management Software (DRM) applied.


Exponential Sums and their Applications

Exponential Sums and their Applications [Pdf/ePub] eBook Author: N.M Korobov
Editor: Springer Science & Business Media
ISBN-10: 9401580324
Size: 701 kb
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Exponential Sums and their Applications by N.M Korobov Book Summary:

The method of exponential sums is a general method enabling the solution of a wide range of problems in the theory of numbers and its applications. This volume presents an exposition of the fundamentals of the theory with the help of examples which show how exponential sums arise and how they are applied in problems of number theory and its applications. The material is divided into three chapters which embrace the classical results of Gauss, and the methods of Weyl, Mordell and Vinogradov; the traditional applications of exponential sums to the distribution of fractional parts, the estimation of the Riemann zeta function; and the theory of congruences and Diophantine equations. Some new applications of exponential sums are also included. It is assumed that the reader has a knowledge of the fundamentals of mathematical analysis and of elementary number theory.

Download or read Exponential Sums and their Applications book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). The method of exponential sums is a general method enabling the solution of a wide range of problems in the theory of numbers and its applications. This volume presents an exposition of the fundamentals of the theory with the help of examples which show how exponential sums arise and how they are applied in problems of number theory and its applications. The material is divided into three chapters which embrace the classical results of Gauss, and the methods of Weyl, Mordell and Vinogradov; the traditional applications of exponential sums to the distribution of fractional parts, the estimation of the Riemann zeta function; and the theory of congruences and Diophantine equations. Some new applications of exponential sums are also included. It is assumed that the reader has a knowledge of the fundamentals of mathematical analysis and of elementary number theory.


The Riemann Zeta-Function

The Riemann Zeta-Function [Pdf/ePub] eBook Author: Aleksandar Ivic
Editor: Courier Corporation
ISBN-10: 0486140040
Size: 1824 kb
Format File: Pdf
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The Riemann Zeta-Function by Aleksandar Ivic Book Summary:

This text covers exponential integrals and sums, 4th power moment, zero-free region, mean value estimates over short intervals, higher power moments, omega results, zeros on the critical line, zero-density estimates, and more. 1985 edition.

Download or read The Riemann Zeta-Function book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). This text covers exponential integrals and sums, 4th power moment, zero-free region, mean value estimates over short intervals, higher power moments, omega results, zeros on the critical line, zero-density estimates, and more. 1985 edition.


Love and Math

Love and Math [Pdf/ePub] eBook Author: Edward Frenkel
Editor: Basic Books
ISBN-10: 0465069959
Size: 1916 kb
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Love and Math by Edward Frenkel Book Summary:

An awesome, globe-spanning, and New York Times best-selling journey through the beauty and power of mathematics What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren't even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry. In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we've never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space. Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man's journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century's leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat's last theorem, that had seemed intractable before. At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.

Download or read Love and Math book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). An awesome, globe-spanning, and New York Times best-selling journey through the beauty and power of mathematics What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren't even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry. In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we've never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space. Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man's journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century's leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat's last theorem, that had seemed intractable before. At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.


Analytic Number Theory, Modular Forms and q-Hypergeometric Series

Analytic Number Theory, Modular Forms and q-Hypergeometric Series [Pdf/ePub] eBook Author: George E. Andrews,Frank Garvan
Editor: Springer
ISBN-10: 3319683764
Size: 1039 kb
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Analytic Number Theory, Modular Forms and q-Hypergeometric Series by George E. Andrews,Frank Garvan Book Summary:

Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory. Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-series identities. Graduate students and researchers will find this volume a valuable resource on new developments in various aspects of number theory.

Download or read Analytic Number Theory, Modular Forms and q-Hypergeometric Series book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory. Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-series identities. Graduate students and researchers will find this volume a valuable resource on new developments in various aspects of number theory.


Trigonometric Sums and Their Applications

Trigonometric Sums and Their Applications [Pdf/ePub] eBook Author: Andrei Raigorodskii,Michael Th. Rassias
Editor: Springer Nature
ISBN-10: 3030379043
Size: 1551 kb
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Trigonometric Sums and Their Applications by Andrei Raigorodskii,Michael Th. Rassias Book Summary:

This volume presents in a unified manner both classic as well as modern research results devoted to trigonometric sums. Such sums play an integral role in the formulation and understanding of a broad spectrum of problems which range over surprisingly many and different research areas. Fundamental and new developments are presented to discern solutions to problems across several scientific disciplines. Graduate students and researchers will find within this book numerous examples and a plethora of results related to trigonometric sums through pure and applied research along with open problems and new directions for future research.

Download or read Trigonometric Sums and Their Applications book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). This volume presents in a unified manner both classic as well as modern research results devoted to trigonometric sums. Such sums play an integral role in the formulation and understanding of a broad spectrum of problems which range over surprisingly many and different research areas. Fundamental and new developments are presented to discern solutions to problems across several scientific disciplines. Graduate students and researchers will find within this book numerous examples and a plethora of results related to trigonometric sums through pure and applied research along with open problems and new directions for future research.


Multiple Zeta Functions, Multiple Polylogarithms and Their Special Values

Multiple Zeta Functions, Multiple Polylogarithms and Their Special Values [Pdf/ePub] eBook Author: Jianqiang Zhao
Editor: World Scientific
ISBN-10: 9814689416
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Multiple Zeta Functions, Multiple Polylogarithms and Their Special Values by Jianqiang Zhao Book Summary:

This is the first introductory book on multiple zeta functions and multiple polylogarithms which are the generalizations of the Riemann zeta function and the classical polylogarithms, respectively, to the multiple variable setting. It contains all the basic concepts and the important properties of these functions and their special values. This book is aimed at graduate students, mathematicians and physicists who are interested in this current active area of research. The book will provide a detailed and comprehensive introduction to these objects, their fascinating properties and interesting relations to other mathematical subjects, and various generalizations such as their q-analogs and their finite versions (by taking partial sums modulo suitable prime powers). Historical notes and exercises are provided at the end of each chapter. Contents:Multiple Zeta FunctionsMultiple Polylogarithms (MPLs)Multiple Zeta Values (MZVs)Drinfeld Associator and Single-Valued MZVsMultiple Zeta Value IdentitiesSymmetrized Multiple Zeta Values (SMZVs)Multiple Harmonic Sums (MHSs) and Alternating VersionFinite Multiple Zeta Values and Finite Euler Sumsq-Analogs of Multiple Harmonic (Star) Sums Readership: Advanced undergraduates and graduate students in mathematics, mathematicians interested in multiple zeta values. Key Features:For the first time, a detailed explanation of the theory of multiple zeta values is given in book form along with numerous illustrations in explicit examplesThe book provides for the first time a comprehensive introduction to multiple polylogarithms and their special values at roots of unity, from the basic definitions to the more advanced topics in current active researchThe book contains a few quite intriguing results relating the special values of multiple zeta functions and multiple polylogarithms to other branches of mathematics and physics, such as knot theory and the theory of motivesMany exercises contain supplementary materials which deepens the reader's understanding of the main text

Download or read Multiple Zeta Functions, Multiple Polylogarithms and Their Special Values book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). This is the first introductory book on multiple zeta functions and multiple polylogarithms which are the generalizations of the Riemann zeta function and the classical polylogarithms, respectively, to the multiple variable setting. It contains all the basic concepts and the important properties of these functions and their special values. This book is aimed at graduate students, mathematicians and physicists who are interested in this current active area of research. The book will provide a detailed and comprehensive introduction to these objects, their fascinating properties and interesting relations to other mathematical subjects, and various generalizations such as their q-analogs and their finite versions (by taking partial sums modulo suitable prime powers). Historical notes and exercises are provided at the end of each chapter. Contents:Multiple Zeta FunctionsMultiple Polylogarithms (MPLs)Multiple Zeta Values (MZVs)Drinfeld Associator and Single-Valued MZVsMultiple Zeta Value IdentitiesSymmetrized Multiple Zeta Values (SMZVs)Multiple Harmonic Sums (MHSs) and Alternating VersionFinite Multiple Zeta Values and Finite Euler Sumsq-Analogs of Multiple Harmonic (Star) Sums Readership: Advanced undergraduates and graduate students in mathematics, mathematicians interested in multiple zeta values. Key Features:For the first time, a detailed explanation of the theory of multiple zeta values is given in book form along with numerous illustrations in explicit examplesThe book provides for the first time a comprehensive introduction to multiple polylogarithms and their special values at roots of unity, from the basic definitions to the more advanced topics in current active researchThe book contains a few quite intriguing results relating the special values of multiple zeta functions and multiple polylogarithms to other branches of mathematics and physics, such as knot theory and the theory of motivesMany exercises contain supplementary materials which deepens the reader's understanding of the main text


Introduction to Analytic Number Theory

Introduction to Analytic Number Theory [Pdf/ePub] eBook Author: Tom M. Apostol
Editor: Springer Science & Business Media
ISBN-10: 1475755791
Size: 635 kb
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Introduction to Analytic Number Theory by Tom M. Apostol Book Summary:

"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages."-—MATHEMATICAL REVIEWS

Download or read Introduction to Analytic Number Theory book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). "This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages."-—MATHEMATICAL REVIEWS


Zeta Regularization Techniques With Applications

Zeta Regularization Techniques With Applications [Pdf/ePub] eBook Author: Andrei A Bytsenko,Emilio Elizalde,Sergei D Odintsov,August Romeo,Sergio Zerbini
Editor: World Scientific
ISBN-10: 9814502987
Size: 1901 kb
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Zeta Regularization Techniques With Applications by Andrei A Bytsenko,Emilio Elizalde,Sergei D Odintsov,August Romeo,Sergio Zerbini Book Summary:

This book is the result of several years of work by the authors on different aspects of zeta functions and related topics. The aim is twofold. On one hand, a considerable number of useful formulas, essential for dealing with the different aspects of zeta-function regularization (analytic continuation, asymptotic expansions), many of which appear here, in book format, for the first time are presented. On the other hand, the authors show explicitly how to make use of such formulas and techniques in practical applications to physical problems of very different nature. Virtually all types of zeta functions are dealt with in the book.

Download or read Zeta Regularization Techniques With Applications book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). This book is the result of several years of work by the authors on different aspects of zeta functions and related topics. The aim is twofold. On one hand, a considerable number of useful formulas, essential for dealing with the different aspects of zeta-function regularization (analytic continuation, asymptotic expansions), many of which appear here, in book format, for the first time are presented. On the other hand, the authors show explicitly how to make use of such formulas and techniques in practical applications to physical problems of very different nature. Virtually all types of zeta functions are dealt with in the book.


Prime Numbers

Prime Numbers [Pdf/ePub] eBook Author: Richard Crandall,Carl B. Pomerance
Editor: Springer Science & Business Media
ISBN-10: 1468493167
Size: 318 kb
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Prime Numbers by Richard Crandall,Carl B. Pomerance Book Summary:

Bridges the gap between theoretical and computational aspects of prime numbers Exercise sections are a goldmine of interesting examples, pointers to the literature and potential research projects Authors are well-known and highly-regarded in the field

Download or read Prime Numbers book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). Bridges the gap between theoretical and computational aspects of prime numbers Exercise sections are a goldmine of interesting examples, pointers to the literature and potential research projects Authors are well-known and highly-regarded in the field


Differential Equations

Differential Equations [Pdf/ePub] eBook Author: Steven G. Krantz
Editor: CRC Press
ISBN-10: 1498735029
Size: 907 kb
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Differential Equations by Steven G. Krantz Book Summary:

Differential Equations: Theory, Technique, and Practice with Boundary Value Problems presents classical ideas and cutting-edge techniques for a contemporary, undergraduate-level, one- or two-semester course on ordinary differential equations. Authored by a widely respected researcher and teacher, the text covers standard topics such as partial differential equations (PDEs), boundary value problems, numerical methods, and dynamical systems. Lively historical notes and mathematical nuggets of information enrich the reading experience by offering perspective on the lives of significant contributors to the discipline. "Anatomy of an Application" sections highlight applications from engineering, physics, and applied science. Problems for review and discovery provide students with open-ended material for further exploration and learning. Streamlined for the interests of engineers, this version: Includes new coverage of Sturm-Liouville theory and problems Discusses PDEs, boundary value problems, and dynamical systems Features an appendix that provides a linear algebra review Augments the substantial and valuable exercise sets Enhances numerous examples to ensure clarity A solutions manual is available with qualifying course adoption. Differential Equations: Theory, Technique, and Practice with Boundary Value Problems delivers a stimulating exposition of modeling and computing, preparing students for higher-level mathematical and analytical thinking.

Download or read Differential Equations book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). Differential Equations: Theory, Technique, and Practice with Boundary Value Problems presents classical ideas and cutting-edge techniques for a contemporary, undergraduate-level, one- or two-semester course on ordinary differential equations. Authored by a widely respected researcher and teacher, the text covers standard topics such as partial differential equations (PDEs), boundary value problems, numerical methods, and dynamical systems. Lively historical notes and mathematical nuggets of information enrich the reading experience by offering perspective on the lives of significant contributors to the discipline. "Anatomy of an Application" sections highlight applications from engineering, physics, and applied science. Problems for review and discovery provide students with open-ended material for further exploration and learning. Streamlined for the interests of engineers, this version: Includes new coverage of Sturm-Liouville theory and problems Discusses PDEs, boundary value problems, and dynamical systems Features an appendix that provides a linear algebra review Augments the substantial and valuable exercise sets Enhances numerous examples to ensure clarity A solutions manual is available with qualifying course adoption. Differential Equations: Theory, Technique, and Practice with Boundary Value Problems delivers a stimulating exposition of modeling and computing, preparing students for higher-level mathematical and analytical thinking.


Abstract Analytic Number Theory

Abstract Analytic Number Theory [Pdf/ePub] eBook Author: John Knopfmacher
Editor: Courier Dover Publications
ISBN-10: 0486169340
Size: 1770 kb
Format File: Pdf
Read: 1770

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Abstract Analytic Number Theory by John Knopfmacher Book Summary:

Innovative study applies classical analytic number theory to nontraditional subjects. Covers arithmetical semigroups and algebraic enumeration problems, arithmetical semigroups with analytical properties of classical type, and analytical properties of other arithmetical systems. 1975 edition.

Download or read Abstract Analytic Number Theory book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). Innovative study applies classical analytic number theory to nontraditional subjects. Covers arithmetical semigroups and algebraic enumeration problems, arithmetical semigroups with analytical properties of classical type, and analytical properties of other arithmetical systems. 1975 edition.


Problems in Analytic Number Theory

Problems in Analytic Number Theory [Pdf/ePub] eBook Author: M. Ram Murty
Editor: Springer Science & Business Media
ISBN-10: 0387723501
Size: 1090 kb
Format File: Pdf
Read: 1090

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Problems in Analytic Number Theory by M. Ram Murty Book Summary:

This informative and exhaustive study gives a problem-solving approach to the difficult subject of analytic number theory. It is primarily aimed at graduate students and senior undergraduates. The goal is to provide a rapid introduction to analytic methods and the ways in which they are used to study the distribution of prime numbers. The book also includes an introduction to p-adic analytic methods. It is ideal for a first course in analytic number theory. The new edition has been completely rewritten, errors have been corrected, and there is a new chapter on the arithmetic progression of primes.

Download or read Problems in Analytic Number Theory book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). This informative and exhaustive study gives a problem-solving approach to the difficult subject of analytic number theory. It is primarily aimed at graduate students and senior undergraduates. The goal is to provide a rapid introduction to analytic methods and the ways in which they are used to study the distribution of prime numbers. The book also includes an introduction to p-adic analytic methods. It is ideal for a first course in analytic number theory. The new edition has been completely rewritten, errors have been corrected, and there is a new chapter on the arithmetic progression of primes.


Non-vanishing of L-Functions and Applications

Non-vanishing of L-Functions and Applications [Pdf/ePub] eBook Author: Ram M. Murty,Kumar V. Murty
Editor: Birkhäuser
ISBN-10: 3034889569
Size: 352 kb
Format File: Pdf
Read: 352

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Non-vanishing of L-Functions and Applications by Ram M. Murty,Kumar V. Murty Book Summary:

This monograph brings together a collection of results on the non-vanishing of L functions. The presentation, though based largely on the original papers, is suitable for independent study. A number of exercises have also been provided to aid in this endeavour. The exercises are of varying difficulty and those which require more effort have been marked with an asterisk. The authors would like to thank the Institut d'Estudis Catalans for their encouragement of this work through the Ferran Sunyer i Balaguer Prize. We would also like to thank the Institute for Advanced Study, Princeton for the excellent conditions which made this work possible, as well as NSERC, NSF and FCAR for funding. Princeton M. Ram Murty August, 1996 V. Kumar Murty Introduction Since the time of Dirichlet and Riemann, the analytic properties of L-functions have been used to establish theorems of a purely arithmetic nature. The distri bution of prime numbers in arithmetic progressions is intimately connected with non-vanishing properties of various L-functions. With the subsequent advent of the Tauberian theory as developed by Wiener and Ikehara, these arithmetical the orems have been shown to be equivalent to the non-vanishing of these L-functions on the line Re(s) = 1. In the 1950's, a new theme was introduced by Birch and Swinnerton-Dyer.

Download or read Non-vanishing of L-Functions and Applications book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). This monograph brings together a collection of results on the non-vanishing of L functions. The presentation, though based largely on the original papers, is suitable for independent study. A number of exercises have also been provided to aid in this endeavour. The exercises are of varying difficulty and those which require more effort have been marked with an asterisk. The authors would like to thank the Institut d'Estudis Catalans for their encouragement of this work through the Ferran Sunyer i Balaguer Prize. We would also like to thank the Institute for Advanced Study, Princeton for the excellent conditions which made this work possible, as well as NSERC, NSF and FCAR for funding. Princeton M. Ram Murty August, 1996 V. Kumar Murty Introduction Since the time of Dirichlet and Riemann, the analytic properties of L-functions have been used to establish theorems of a purely arithmetic nature. The distri bution of prime numbers in arithmetic progressions is intimately connected with non-vanishing properties of various L-functions. With the subsequent advent of the Tauberian theory as developed by Wiener and Ikehara, these arithmetical the orems have been shown to be equivalent to the non-vanishing of these L-functions on the line Re(s) = 1. In the 1950's, a new theme was introduced by Birch and Swinnerton-Dyer.