Sum Formulas Of Multiple Zeta Value With Even Arguments And Polynomial Weights

Download Sum Formulas Of Multiple Zeta Value With Even Arguments And Polynomial Weights full books in PDF, epub, and Kindle. Read online Sum Formulas Of Multiple Zeta Value With Even Arguments And Polynomial Weights ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Multiple Zeta Functions, Multiple Polylogarithms And Their Special Values

Author : Jianqiang Zhao
Publisher : World Scientific
ISBN 13 : 9814689416
Total Pages : 618 pages
Book Rating : 4.8/5 (146 download)

DOWNLOAD NOW!

Book Synopsis Multiple Zeta Functions, Multiple Polylogarithms And Their Special Values by : Jianqiang Zhao

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.

Introduction to Vassiliev Knot Invariants

Author : S. Chmutov
Publisher : Cambridge University Press
ISBN 13 : 1107020832
Total Pages : 521 pages
Book Rating : 4.1/5 (7 download)

DOWNLOAD NOW!

Book Synopsis Introduction to Vassiliev Knot Invariants by : S. Chmutov

Download or read book Introduction to Vassiliev Knot Invariants written by S. Chmutov and published by Cambridge University Press. This book was released on 2012-05-24 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed exposition of the theory with an emphasis on its combinatorial aspects.

Generatingfunctionology

Author : Herbert S. Wilf
Publisher : Elsevier
ISBN 13 : 1483276635
Total Pages : 193 pages
Book Rating : 4.4/5 (832 download)

DOWNLOAD NOW!

Book Synopsis Generatingfunctionology by : Herbert S. Wilf

Download or read book Generatingfunctionology written by Herbert S. Wilf and published by Elsevier. This book was released on 2014-05-10 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generatingfunctionology provides information pertinent to generating functions and some of their uses in discrete mathematics. This book presents the power of the method by giving a number of examples of problems that can be profitably thought about from the point of view of generating functions. Organized into five chapters, this book begins with an overview of the basic concepts of a generating function. This text then discusses the different kinds of series that are widely used as generating functions. Other chapters explain how to make much more precise estimates of the sizes of the coefficients of power series based on the analyticity of the function that is represented by the series. This book discusses as well the applications of the theory of generating functions to counting problems. The final chapter deals with the formal aspects of the theory of generating functions. This book is a valuable resource for mathematicians and students.

Bernoulli Numbers and Zeta Functions

Author : Tsuneo Arakawa
Publisher : Springer
ISBN 13 : 4431549196
Total Pages : 278 pages
Book Rating : 4.4/5 (315 download)

DOWNLOAD NOW!

Book Synopsis Bernoulli Numbers and Zeta Functions by : Tsuneo Arakawa

Download or read book Bernoulli Numbers and Zeta Functions written by Tsuneo Arakawa and published by Springer. This book was released on 2014-07-11 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers. The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advanced topics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers; a formula for Bernoulli numbers by Stirling numbers; the Clausen–von Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of p-adic measures; the Euler–Maclaurin summation formula; the functional equation of the Riemann zeta function and the Dirichlet L functions, and their special values at suitable integers; various formulas of exponential sums expressed by generalized Bernoulli numbers; the relation between ideal classes of orders of quadratic fields and equivalence classes of binary quadratic forms; class number formula for positive definite binary quadratic forms; congruences between some class numbers and Bernoulli numbers; simple zeta functions of prehomogeneous vector spaces; Hurwitz numbers; Barnes multiple zeta functions and their special values; the functional equation of the doub le zeta functions; and poly-Bernoulli numbers. An appendix by Don Zagier on curious and exotic identities for Bernoulli numbers is also supplied. This book will be enjoyable both for amateurs and for professional researchers. Because the logical relations between the chapters are loosely connected, readers can start with any chapter depending on their interests. The expositions of the topics are not always typical, and some parts are completely new.

The 1-2-3 of Modular Forms

Author : Jan Hendrik Bruinier
Publisher : Springer Science & Business Media
ISBN 13 : 3540741194
Total Pages : 273 pages
Book Rating : 4.5/5 (47 download)

DOWNLOAD NOW!

Book Synopsis The 1-2-3 of Modular Forms by : Jan Hendrik Bruinier

Download or read book The 1-2-3 of Modular Forms written by Jan Hendrik Bruinier and published by Springer Science & Business Media. This book was released on 2008-02-10 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.

Zeta and Q-Zeta Functions and Associated Series and Integrals

Author : H. M. Srivastava
Publisher : Elsevier
ISBN 13 : 0123852188
Total Pages : 675 pages
Book Rating : 4.1/5 (238 download)

DOWNLOAD NOW!

Book Synopsis Zeta and Q-Zeta Functions and Associated Series and Integrals by : H. M. Srivastava

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

The Riemann Zeta-Function

Author : Anatoly A. Karatsuba
Publisher : Walter de Gruyter
ISBN 13 : 3110886146
Total Pages : 409 pages
Book Rating : 4.1/5 (18 download)

DOWNLOAD NOW!

Book Synopsis The Riemann Zeta-Function by : Anatoly A. Karatsuba

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

Handbook of Mathematical Functions

Author : Milton Abramowitz
Publisher : Courier Corporation
ISBN 13 : 9780486612720
Total Pages : 1068 pages
Book Rating : 4.6/5 (127 download)

DOWNLOAD NOW!

Book Synopsis Handbook of Mathematical Functions by : Milton Abramowitz

Download or read book Handbook of Mathematical Functions written by Milton Abramowitz and published by Courier Corporation. This book was released on 1965-01-01 with total page 1068 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extensive summary of mathematical functions that occur in physical and engineering problems

Summability Calculus

Author : Ibrahim M. Alabdulmohsin
Publisher : Springer
ISBN 13 : 3319746480
Total Pages : 168 pages
Book Rating : 4.3/5 (197 download)

DOWNLOAD NOW!

Book Synopsis Summability Calculus by : Ibrahim M. Alabdulmohsin

Download or read book Summability Calculus written by Ibrahim M. Alabdulmohsin and published by Springer. This book was released on 2018-03-07 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the foundations of "summability calculus", which is a comprehensive theory of fractional finite sums. It fills an important gap in the literature by unifying and extending disparate historical results. It also presents new material that has not been published before. Importantly, it shows how the study of fractional finite sums benefits from and contributes to many areas of mathematics, such as divergent series, numerical integration, approximation theory, asymptotic methods, special functions, series acceleration, Fourier analysis, the calculus of finite differences, and information theory. As such, it appeals to a wide audience of mathematicians whose interests include the study of special functions, summability theory, analytic number theory, series and sequences, approximation theory, asymptotic expansions, or numerical methods. Richly illustrated, it features chapter summaries, and includes numerous examples and exercises. The content is mostly developed from scratch using only undergraduate mathematics, such as calculus and linear algebra.

CRC Standard Mathematical Tables and Formulae, 32nd Edition

Author : Daniel Zwillinger
Publisher : CRC Press
ISBN 13 : 1439835500
Total Pages : 792 pages
Book Rating : 4.4/5 (398 download)

DOWNLOAD NOW!

Book Synopsis CRC Standard Mathematical Tables and Formulae, 32nd Edition by : Daniel Zwillinger

Download or read book CRC Standard Mathematical Tables and Formulae, 32nd Edition written by Daniel Zwillinger and published by CRC Press. This book was released on 2011-06-22 with total page 792 pages. Available in PDF, EPUB and Kindle. Book excerpt: With over 6,000 entries, CRC Standard Mathematical Tables and Formulae, 32nd Edition continues to provide essential formulas, tables, figures, and descriptions, including many diagrams, group tables, and integrals not available online. This new edition incorporates important topics that are unfamiliar to some readers, such as visual proofs and sequences, and illustrates how mathematical information is interpreted. Material is presented in a multisectional format, with each section containing a valuable collection of fundamental tabular and expository reference material. New to the 32nd Edition A new chapter on Mathematical Formulae from the Sciences that contains the most important formulae from a variety of fields, including acoustics, astrophysics, epidemiology, finance, statistical mechanics, and thermodynamics New material on contingency tables, estimators, process capability, runs test, and sample sizes New material on cellular automata, knot theory, music, quaternions, and rational trigonometry Updated and more streamlined tables Retaining the successful format of previous editions, this comprehensive handbook remains an invaluable reference for professionals and students in mathematical and scientific fields.

Introduction to $p$-adic Analytic Number Theory

Author : M. Ram Murty
Publisher : American Mathematical Soc.
ISBN 13 : 0821847740
Total Pages : 162 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Introduction to $p$-adic Analytic Number Theory by : M. Ram Murty

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.

Not Always Buried Deep

Author : Paul Pollack
Publisher : American Mathematical Soc.
ISBN 13 : 0821848801
Total Pages : 322 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Not Always Buried Deep by : Paul Pollack

Download or read book Not Always Buried Deep written by Paul Pollack and published by American Mathematical Soc.. This book was released on 2009-10-14 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number theory is one of the few areas of mathematics where problems of substantial interest can be fully described to someone with minimal mathematical background. Solving such problems sometimes requires difficult and deep methods. But this is not a universal phenomenon; many engaging problems can be successfully attacked with little more than one's mathematical bare hands. In this case one says that the problem can be solved in an elementary way. Such elementary methods and the problems to which they apply are the subject of this book. Not Always Buried Deep is designed to be read and enjoyed by those who wish to explore elementary methods in modern number theory. The heart of the book is a thorough introduction to elementary prime number theory, including Dirichlet's theorem on primes in arithmetic progressions, the Brun sieve, and the Erdos-Selberg proof of the prime number theorem. Rather than trying to present a comprehensive treatise, Pollack focuses on topics that are particularly attractive and accessible. Other topics covered include Gauss's theory of cyclotomy and its applications to rational reciprocity laws, Hilbert's solution to Waring's problem, and modern work on perfect numbers. The nature of the material means that little is required in terms of prerequisites: The reader is expected to have prior familiarity with number theory at the level of an undergraduate course and a first course in modern algebra (covering groups, rings, and fields). The exposition is complemented by over 200 exercises and 400 references.

Combinatorics: The Art of Counting

Author : Bruce E. Sagan
Publisher : American Mathematical Soc.
ISBN 13 : 1470460327
Total Pages : 304 pages
Book Rating : 4.4/5 (74 download)

DOWNLOAD NOW!

Book Synopsis Combinatorics: The Art of Counting by : Bruce E. Sagan

Download or read book Combinatorics: The Art of Counting written by Bruce E. Sagan and published by American Mathematical Soc.. This book was released on 2020-10-16 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance. The book assumes minimal background, and a first course in abstract algebra should suffice. The exposition is very reader friendly: keeping a moderate pace, using lots of examples, emphasizing recurring themes, and frankly expressing the delight the author takes in mathematics in general and combinatorics in particular.

Asymptotics and Borel Summability

Author : Ovidiu Costin
Publisher : CRC Press
ISBN 13 : 1420070320
Total Pages : 266 pages
Book Rating : 4.4/5 (2 download)

DOWNLOAD NOW!

Book Synopsis Asymptotics and Borel Summability by : Ovidiu Costin

Download or read book Asymptotics and Borel Summability written by Ovidiu Costin and published by CRC Press. This book was released on 2008-12-04 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, tr

Analytic Combinatorics

Author : Philippe Flajolet
Publisher : Cambridge University Press
ISBN 13 : 1139477161
Total Pages : 825 pages
Book Rating : 4.1/5 (394 download)

DOWNLOAD NOW!

Book Synopsis Analytic Combinatorics by : Philippe Flajolet

Download or read book Analytic Combinatorics written by Philippe Flajolet and published by Cambridge University Press. This book was released on 2009-01-15 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.

Mathematics and Computation

Author : Avi Wigderson
Publisher : Princeton University Press
ISBN 13 : 0691189137
Total Pages : 434 pages
Book Rating : 4.6/5 (911 download)

DOWNLOAD NOW!

Book Synopsis Mathematics and Computation by : Avi Wigderson

Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Prime-detecting Sieves

Author : Glyn Harman
Publisher : Princeton University Press
ISBN 13 : 069112437X
Total Pages : 378 pages
Book Rating : 4.6/5 (911 download)

DOWNLOAD NOW!

Book Synopsis Prime-detecting Sieves by : Glyn Harman

Download or read book Prime-detecting Sieves written by Glyn Harman and published by Princeton University Press. This book was released on 2007-08-05 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book seeks to describe the rapid development in recent decades of sieve methods able to detect prime numbers. The subject began with Eratosthenes in antiquity, took on new shape with Legendre's form of the sieve, was substantially reworked by Ivan M. Vinogradov and Yuri V. Linnik, but came into its own with Robert C. Vaughan and important contributions from others, notably Roger Heath-Brown and Henryk Iwaniec. Prime-Detecting Sieves breaks new ground by bringing together several different types of problems that have been tackled with modern sieve methods and by discussing the ideas common to each, in particular the use of Type I and Type II information. No other book has undertaken such a systematic treatment of prime-detecting sieves. Among the many topics Glyn Harman covers are primes in short intervals, the greatest prime factor of the sequence of shifted primes, Goldbach numbers in short intervals, the distribution of Gaussian primes, and the recent work of John Friedlander and Iwaniec on primes that are a sum of a square and a fourth power, and Heath-Brown's work on primes represented as a cube plus twice a cube. This book contains much that is accessible to beginning graduate students, yet also provides insights that will benefit established researchers.