Various Aspects Of Multiple Zeta Functions

DOWNLOAD

Download Various Aspects Of Multiple Zeta Functions PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Various Aspects Of Multiple Zeta Functions book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Various Aspects Of Multiple Zeta Functions

DOWNLOAD
Author : Hidehiko Mishou
language : en
Publisher: Advanced Studies in Pure Mathe
Release Date : 2020

Various Aspects Of Multiple Zeta Functions written by Hidehiko Mishou and has been published by Advanced Studies in Pure Mathe this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Mathematics categories.

This volume is the proceedings of the international conference 'Various Aspects of Multiple Zeta Functions' in honor of Professor Kohji Matsumoto's 60th birthday held at Nagoya University, Japan, during August 21 to 25, 2017.The present volume consists of 15 research papers on various recent topics about multiple zeta-functions, which include not only actually multivariate cases but also single-variable cases, additive and multiplicative number theory, and poly-Bernoulli numbers and polynomials.The editors believe that this volume represents the major part of the contributions presented in the conference, and hope that the volume is useful for all researchers and students who are interested in this fruitful research field.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America

Multiple Zeta Functions Multiple Polylogarithms And Their Special Values

DOWNLOAD
Author : Jianqiang Zhao
language : en
Publisher: World Scientific
Release Date : 2016-03-07

Multiple Zeta Functions Multiple Polylogarithms And Their Special Values written by Jianqiang Zhao and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-07 with Mathematics categories.

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.

The Theory Of Zeta Functions Of Root Systems

DOWNLOAD
Author : Yasushi Komori
language : en
Publisher: Springer Nature
Release Date : 2024-01-02

The Theory Of Zeta Functions Of Root Systems written by Yasushi Komori and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-02 with Mathematics categories.

The contents of this book was created by the authors as a simultaneous generalization of Witten zeta-functions, Mordell–Tornheim multiple zeta-functions, and Euler–Zagier multiple zeta-functions. Zeta-functions of root systems are defined by certain multiple series, given in terms of root systems. Therefore, they intrinsically have the action of associated Weyl groups. The exposition begins with a brief introduction to the theory of Lie algebras and root systems and then provides the definition of zeta-functions of root systems, explicit examples associated with various simple Lie algebras, meromorphic continuation and recursive analytic structure described by Dynkin diagrams, special values at integer points, functional relations, and the background given by the action of Weyl groups. In particular, an explicit form of Witten’s volume formula is provided. It is shown that various relations among special values of Euler–Zagier multiple zeta-functions—which usually are called multiple zeta values (MZVs) and are quite important in connection with Zagier’s conjecture—are just special cases of various functional relations among zeta-functions of root systems. The authors further provide other applications to the theory of MZVs and also introduce generalizations with Dirichlet characters, and with certain congruence conditions. The book concludes with a brief description of other relevant topics.

Zeta Functions Topology And Quantum Physics

DOWNLOAD
Author : Takashi Aoki
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-10

Zeta Functions Topology And Quantum Physics written by Takashi Aoki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-10 with Mathematics categories.

This volume contains papers by invited speakers of the symposium "Zeta Functions, Topology and Quantum Physics" held at Kinki U- versity in Osaka, Japan, during the period of March 3-6, 2003. The aims of this symposium were to establish mutual understanding and to exchange ideas among researchers working in various fields which have relation to zeta functions and zeta values. We are very happy to add this volume to the series Developments in Mathematics from Springer. In this respect, Professor Krishnaswami Alladi helped us a lot by showing his keen and enthusiastic interest in publishing this volume and by contributing his paper with Alexander Berkovich. We gratefully acknowledge financial support from Kinki University. We would like to thank Professor Megumu Munakata, Vice-Rector of Kinki University, and Professor Nobuki Kawashima, Director of School of Interdisciplinary Studies of Science and Engineering, Kinki Univ- sity, for their interest and support. We also thank John Martindale of Springer for his excellent editorial work.

Zeta And Q Zeta Functions And Associated Series And Integrals

DOWNLOAD
Author : Hari M Srivastava
language : en
Publisher: Elsevier
Release Date : 2011-10-11

Zeta And Q Zeta Functions And Associated Series And Integrals written by Hari M Srivastava and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-11 with Mathematics categories.

Zeta and q-Zeta Functions and Associated Series and Integrals is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions. Many of the chapters and sections of the book have been significantly modified or rewritten, and a new chapter on the theory and applications of the basic (or q-) extensions of various special functions is included. This book will be invaluable because it covers not only detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions, but stimulating historical accounts of a large number of problems and well-classified tables of series and integrals. - Detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions

Number Theory

DOWNLOAD
Author : Takashi Aoki
language : en
Publisher: World Scientific
Release Date : 2010

Number Theory written by Takashi Aoki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

This volume aims at collecting survey papers which give broad and enlightening perspectives of various aspects of number theory. Kitaoka''s paper is a continuation of his earlier paper published in the last proceedings and pushes the research forward. Browning''s paper introduces a new direction of research on analytic number theory OCo quantitative theory of some surfaces and Bruedern et al ''s paper details state-of-the-art affairs of additive number theory. There are two papers on modular forms OCo Kohnen''s paper describes generalized modular forms (GMF) which has some applications in conformal field theory, while Liu''s paper is very useful for readers who want to have a quick introduction to Maass forms and some analytic-number-theoretic problems related to them. Matsumoto et al ''s paper gives a very thorough survey on functional relations of root system zeta-functions, HoshiOCoMiyake''s paper is a continuation of Miyake''s long and fruitful research on generic polynomials and gives rise to related Diophantine problems, and Jia''s paper surveys some dynamical aspects of a special arithmetic function connected with the distribution of prime numbers. There are two papers of collections of problems by Shparlinski on exponential and character sums and Schinzel on polynomials which will serve as an aid for finding suitable research problems. Yamamura''s paper is a complete bibliography on determinant expressions for a certain class number and will be useful to researchers. Thus the book gives a good-balance of classical and modern aspects in number theory and will be useful to researchers including enthusiastic graduate students. Sample Chapter(s). Chapter 1: Resent Progress on the Quantitative Arithmetic of Del Pezzo Surfaces (329 KB). Contents: Recent Progress on the Quantitative Arithmetic of Del Pezzo Surfaces (T D Browning); Additive Representation in Thin Sequences, VIII: Diophantine Inequalities in Review (J Brdern et al.); Recent Progress on Dynamics of a Special Arithmetic Function (C-H Jia); Some Diophantine Problems Arising from the Isomorphism Problem of Generic Polynomials (A Hoshi & K Miyake); A Statistical Relation of Roots of a Polynomial in Different Local Fields II (Y Kitaoka); Generalized Modular Functions and Their Fourier Coefficients (W Kohnen); Functional Relations for Zeta-Functions of Root Systems (Y Komori et al.); A Quick Introduction to Maass Forms (J-Y Liu); The Number of Non-Zero Coefficients of a Polynomial-Solved and Unsolved Problems (A Schinzel); Open Problems on Exponential and Character Sums (I E Shparlinski); Errata to OC A General Modular Relation in Analytic Number TheoryOCO (H Tsukada); Bibliography on Determinantal Expressions of Relative Class Numbers of Imaginary Abelian Number Fields (K Yamamura). Readership: Graduate students and researchers in mathematics.

Number Theory Dreaming In Dreams Proceedings Of The 5th China Japan Seminar

DOWNLOAD
Author : Shigeru Kanemitsu
language : en
Publisher: World Scientific
Release Date : 2009-11-26

Number Theory Dreaming In Dreams Proceedings Of The 5th China Japan Seminar written by Shigeru Kanemitsu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-26 with Mathematics categories.

This volume aims at collecting survey papers which give broad and enlightening perspectives of various aspects of number theory.Kitaoka's paper is a continuation of his earlier paper published in the last proceedings and pushes the research forward. Browning's paper introduces a new direction of research on analytic number theory — quantitative theory of some surfaces and Bruedern et al's paper details state-of-the-art affairs of additive number theory. There are two papers on modular forms — Kohnen's paper describes generalized modular forms (GMF) which has some applications in conformal field theory, while Liu's paper is very useful for readers who want to have a quick introduction to Maass forms and some analytic-number-theoretic problems related to them. Matsumoto et al's paper gives a very thorough survey on functional relations of root system zeta-functions, Hoshi-Miyake's paper is a continuation of Miyake's long and fruitful research on generic polynomials and gives rise to related Diophantine problems, and Jia's paper surveys some dynamical aspects of a special arithmetic function connected with the distribution of prime numbers. There are two papers of collections of problems by Shparlinski on exponential and character sums and Schinzel on polynomials which will serve as an aid for finding suitable research problems. Yamamura's paper is a complete bibliography on determinant expressions for a certain class number and will be useful to researchers.Thus the book gives a good-balance of classical and modern aspects in number theory and will be useful to researchers including enthusiastic graduate students.

Zeta And Q Zeta Functions And Associated Series And Integrals

DOWNLOAD
Author : H. M. Srivastava
language : en
Publisher: Elsevier
Release Date : 2011-10-25

Zeta And Q Zeta Functions And Associated Series And Integrals written by H. M. Srivastava and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-25 with Mathematics categories.

Zeta and q-Zeta Functions and Associated Series and Integrals is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions. Many of the chapters and sections of the book have been significantly modified or rewritten, and a new chapter on the theory and applications of the basic (or q-) extensions of various special functions is included. This book will be invaluable because it covers not only detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions, but stimulating historical accounts of a large number of problems and well-classified tables of series and integrals. Detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions

The Theory Of Multiple Zeta Values With Applications In Combinatorics

DOWNLOAD
Author : Minking Eie
language : en
Publisher: World Scientific
Release Date : 2013-05-22

The Theory Of Multiple Zeta Values With Applications In Combinatorics written by Minking Eie and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-22 with Mathematics categories.

This is the first book on the theory of multiple zeta values since its birth around 1994. Readers will find that the shuffle products of multiple zeta values are applied to complicated counting problems in combinatorics, and numerous interesting identities are produced that are ready to be used. This will provide a powerful tool to deal with problems in multiple zeta values, both in evaluations and shuffle relations. The volume will benefit graduate students doing research in number theory.

Series Associated With The Zeta And Related Functions

DOWNLOAD
Author : Hari M. Srivastava
language : en
Publisher: Springer Science & Business Media
Release Date : 2001

Series Associated With The Zeta And Related Functions written by Hari M. Srivastava and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

In recent years there has been an increasing interest in problems involving closed form evaluations of (and representations of the Riemann Zeta function at positive integer arguments as) various families of series associated with the Riemann Zeta function ((s), the Hurwitz Zeta function ((s,a), and their such extensions and generalizations as (for example) Lerch's transcendent (or the Hurwitz-Lerch Zeta function) iI>(z, s, a). Some of these developments have apparently stemmed from an over two-century-old theorem of Christian Goldbach (1690-1764), which was stated in a letter dated 1729 from Goldbach to Daniel Bernoulli (1700-1782), from recent rediscoveries of a fairly rapidly convergent series representation for ((3), which is actually contained in a 1772 paper by Leonhard Euler (1707-1783), and from another known series representation for ((3), which was used by Roger Apery (1916-1994) in 1978 in his celebrated proof of the irrationality of ((3). This book is motivated essentially by the fact that the theories and applications of the various methods and techniques used in dealing with many different families of series associated with the Riemann Zeta function and its aforementioned relatives are to be found so far only"in widely scattered journal articles. Thus our systematic (and unified) presentation of these results on the evaluation and representation of the Zeta and related functions is expected to fill a conspicuous gap in the existing books dealing exclusively with these Zeta functions.