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Author : 曾晏薇
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (111 download)
Download or read book Euler Sums with Two Branches and Sum Formulas of Multiple Zeta Values written by 曾晏薇 and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jianqiang Zhao
Publisher : World Scientific
ISBN 13 : 9814689416
Total Pages : 618 pages
Book Rating : 4.8/5 (146 download)
Download or read book Multiple Zeta Functions, Multiple Polylogarithms And Their Special Values written by Jianqiang Zhao and published by World Scientific. This book was released on 2016-03-07 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Minking Eie
Publisher : World Scientific
ISBN 13 : 9814472654
Total Pages : 313 pages
Book Rating : 4.8/5 (144 download)
Download or read book The Theory Of Multiple Zeta Values With Applications In Combinatorics written by Minking Eie and published by World Scientific. This book was released on 2013-05-22 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : H. M. Srivastava
Publisher : Elsevier
ISBN 13 : 0123852188
Total Pages : 675 pages
Book Rating : 4.1/5 (238 download)
Download or read book Zeta and Q-Zeta Functions and Associated Series and Integrals written by H. M. Srivastava and published by Elsevier. This book was released on 2011-10-25 with total page 675 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author : 謝宜庭
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (968 download)
Download or read book Twisted Sum Formulas of Multiple Zeta Values written by 謝宜庭 and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hari M. Srivastava
Publisher : Springer Science & Business Media
ISBN 13 : 9780792370543
Total Pages : 408 pages
Book Rating : 4.3/5 (75 download)
Download or read book Series Associated With the Zeta and Related Functions written by Hari M. Srivastava and published by Springer Science & Business Media. This book was released on 2001 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Some Weighted Sum Formulas of Multiple Zeta Values written by and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : 蕭秀如
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (111 download)
Download or read book Weighted Sum Formulas of Different Depths of Multiple Zeta Values written by 蕭秀如 and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cyclic Sum Formulas for Multiple Zeta Values and Multiple Zeta-Star Values written by and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : 江奇璋
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (987 download)
Download or read book Sum formulas of multiple zeta value with even arguments and polynomial weights written by 江奇璋 and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bernoulli Identities and Weighted Sum Formulas of Multiple Zeta Values written by and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : 許嘉峰
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (12 download)
Download or read book Relations Of Two Double-weighted Sums Of Multiple Zeta Values written by 許嘉峰 and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Minking Eie
Publisher : World Scientific
ISBN 13 : 9812835180
Total Pages : 295 pages
Book Rating : 4.8/5 (128 download)
Download or read book Topics in Number Theory written by Minking Eie and published by World Scientific. This book was released on 2009 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a first-ever textbook written in English about the theory of modular forms and Jacobi forms of several variables. It contains the classical theory as well as a new theory on Jacobi forms over Cayley numbers developed by the author from 1990 to 2000. Applications to the classical Euler sums are of special interest to those who are eager to evaluate double Euler sums or more general multiple zeta values. The celebrated sum formula proved by Granville in 1997 is generalized to a more general form here.
Author : Leonard Lewin
Publisher : American Mathematical Soc.
ISBN 13 : 0821816349
Total Pages : 432 pages
Book Rating : 4.8/5 (218 download)
Download or read book Structural Properties of Polylogarithms written by Leonard Lewin and published by American Mathematical Soc.. This book was released on 1991 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: About ten years ago, the handful of peculiar numerical diogarithmic identities, known since the time of Euler and Landen, gave rise to new discoveries concerning cyclotomic equations and related polylogarithmic ladders. These discoveries were made mostly by the methods of classical analysis, with help from machine computation. About the same time, starting with Bloch's studies on the application of the dilogarithm in algebraic K-theory and algebraic geometry, many important discoveries were made in diverse areas. This book seeks to provide a synthesis of these two streams of thought. In addition to an account of ladders and their association with functional equations, the chapters include applications to volume calculations in Lobatchevsky geometry, relations to partition theory, connections with Clausen's function, new functional equations, and applications to K-theory and other branches of abstract algebra. This rapidly-expanding field is brought up to date with two appendices, and the book concludes with an extensive bibliography of recent publications. About two-thirds of the material is accessible to mathematicians and scientists in many areas, while the remainder requires more specialized background in abstract algebra.
Author : Anatoly A. Karatsuba
Publisher : Walter de Gruyter
ISBN 13 : 3110886146
Total Pages : 409 pages
Book Rating : 4.1/5 (18 download)
Download or read book The Riemann Zeta-Function written by Anatoly A. Karatsuba and published by Walter de Gruyter. This book was released on 2011-05-03 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author : John Riordan
Publisher : Princeton University Press
ISBN 13 : 1400854334
Total Pages : 257 pages
Book Rating : 4.4/5 (8 download)
Download or read book An Introduction to Combinatorial Analysis written by John Riordan and published by Princeton University Press. This book was released on 2014-07-14 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces combinatorial analysis to the beginning student. The author begins with the theory of permutation and combinations and their applications to generating functions. In subsequent chapters, he presents Bell polynomials; the principle of inclusion and exclusion; the enumeration of permutations in cyclic representation; the theory of distributions; partitions, compositions, trees and linear graphs; and the enumeration of restricted permutations. Originally published in 1980. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author : M. Ram Murty
Publisher : American Mathematical Soc.
ISBN 13 : 0821847740
Total Pages : 162 pages
Book Rating : 4.8/5 (218 download)
Download or read book Introduction to $p$-adic Analytic Number Theory written by M. Ram Murty and published by American Mathematical Soc.. This book was released on 2009-02-09 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an elementary introduction to $p$-adic analysis from the number theory perspective. With over 100 exercises included, it will acquaint the non-expert to the basic ideas of the theory and encourage the novice to enter this fertile field of research. The main focus of the book is the study of $p$-adic $L$-functions and their analytic properties. It begins with a basic introduction to Bernoulli numbers and continues with establishing the Kummer congruences. These congruences are then used to construct the $p$-adic analog of the Riemann zeta function and $p$-adic analogs of Dirichlet's $L$-functions. Featured is a chapter on how to apply the theory of Newton polygons to determine Galois groups of polynomials over the rational number field. As motivation for further study, the final chapter introduces Iwasawa theory.
