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Zeta And Q Zeta Functions And Associated Series And Integrals

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Zeta and q Zeta Functions and Associated Series and Integrals

Zeta and q Zeta Functions and Associated Series and Integrals Book
Author : H. M. Srivastava,Junesang Choi
Publisher : Elsevier
Release : 2011-10-11
ISBN : 0123852196
Language : En, Es, Fr & De

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Book Description :

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

Zeta and Q Zeta Functions and Associated Series and Integrals

Zeta and Q Zeta Functions and Associated Series and Integrals Book
Author : H. M. Srivastava,Choi Junesang
Publisher : Elsevier
Release : 2012
ISBN : 0123852188
Language : En, Es, Fr & De

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Book Description :

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

Series Associated With the Zeta and Related Functions

Series Associated With the Zeta and Related Functions Book
Author : Hari M. Srivastava,Junesang Choi
Publisher : Springer Science & Business Media
Release : 2001
ISBN : 9780792370543
Language : En, Es, Fr & De

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Book Description :

Designed as a reference work and also as a graduate-level textbook, this volume presents an up-to-date and comprehensive account of the theories and applications of the various methods and techniques used in dealing with problems involving closed-form evaluations of (and representations of the Riemann Zeta function at positive integer arguments as) numerous families of series associated with the Riemann Zeta function, the Hurwitz Zeta function, and their extensions and generalizations such as Lerch's transcendent (or the Hurwitz-Lerch Zeta function). Audience: This book is intended for professional mathematicians and graduate students in mathematical sciences (both pure and applied).

Integral Transforms and Operational Calculus

Integral Transforms and Operational Calculus Book
Author : H. M. Srivastava
Publisher : MDPI
Release : 2019-11-20
ISBN : 303921618X
Language : En, Es, Fr & De

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Book Description :

Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. This Special Issue contains a total of 36 carefully-selected and peer-reviewed articles which are authored by established researchers from many countries. Included in this Special Issue are review, expository and original research articles dealing with the recent advances on the topics of integral transforms and operational calculus as well as their multidisciplinary applications

Analytic Number Theory Approximation Theory and Special Functions

Analytic Number Theory  Approximation Theory  and Special Functions Book
Author : Gradimir V. Milovanović,Michael Th. Rassias
Publisher : Springer
Release : 2014-07-08
ISBN : 149390258X
Language : En, Es, Fr & De

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Book Description :

This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics and other computational and applied sciences.

Generalized Mathieu Series

Generalized Mathieu Series Book
Author : Živorad Tomovski,Delčo Leškovski,Stefan Gerhold
Publisher : Springer Nature
Release : 2021-11-15
ISBN : 3030848175
Language : En, Es, Fr & De

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Book Description :

The Mathieu series is a functional series introduced by Émile Léonard Mathieu for the purposes of his research on the elasticity of solid bodies. Bounds for this series are needed for solving biharmonic equations in a rectangular domain. In addition to Tomovski and his coauthors, Pogany, Cerone, H. M. Srivastava, J. Choi, etc. are some of the known authors who published results concerning the Mathieu series, its generalizations and their alternating variants. Applications of these results are given in classical, harmonic and numerical analysis, analytical number theory, special functions, mathematical physics, probability, quantum field theory, quantum physics, etc. Integral representations, analytical inequalities, asymptotic expansions and behaviors of some classes of Mathieu series are presented in this book. A systematic study of probability density functions and probability distributions associated with the Mathieu series, its generalizations and Planck’s distribution is also presented. The book is addressed at graduate and PhD students and researchers in mathematics and physics who are interested in special functions, inequalities and probability distributions.

Mathematical Analysis in Interdisciplinary Research

Mathematical Analysis in Interdisciplinary Research Book
Author : Ioannis N. Parasidis
Publisher : Springer Nature
Release : 2022-08-17
ISBN : 3030847217
Language : En, Es, Fr & De

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Book Description :

Download Mathematical Analysis in Interdisciplinary Research book written by Ioannis N. Parasidis, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Approximation Theory and Analytic Inequalities

Approximation Theory and Analytic Inequalities Book
Author : Themistocles M. Rassias
Publisher : Springer Nature
Release : 2021-07-21
ISBN : 3030606228
Language : En, Es, Fr & De

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Book Description :

This contributed volume focuses on various important areas of mathematics in which approximation methods play an essential role. It features cutting-edge research on a wide spectrum of analytic inequalities with emphasis on differential and integral inequalities in the spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a plethora of applications, making this work a valuable resource. The reader will be exposed to convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point theory for operators, PDEs, fractional integral inequalities, multidimensional numerical integration, Gauss–Jacobi and Hermite–Hadamard type inequalities, Hilbert-type inequalities, and Ulam’s stability of functional equations. Contributions have been written by eminent researchers, providing up-to-date information and several results which may be useful to a wide readership including graduate students and researchers working in mathematics, physics, economics, operational research, and their interconnections.

Current Trends in Symmetric Polynomials with their Applications

Current Trends in Symmetric Polynomials with their Applications Book
Author : Taekyun Kim
Publisher : MDPI
Release : 2019-10-15
ISBN : 3039216201
Language : En, Es, Fr & De

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Book Description :

This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and includes the most recent advances made in the area of symmetric functions and polynomials.

Multiple Zeta Functions Multiple Polylogarithms and Their Special Values

Multiple Zeta Functions  Multiple Polylogarithms and Their Special Values Book
Author : Jianqiang Zhao
Publisher : World Scientific
Release : 2016-03-07
ISBN : 9814689416
Language : En, Es, Fr & De

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Book Description :

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

Zeta Functions of Groups and Rings

Zeta Functions of Groups and Rings Book
Author : Marcus du Sautoy,Luke Woodward
Publisher : Springer Science & Business Media
Release : 2008
ISBN : 354074701X
Language : En, Es, Fr & De

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Book Description :

Thestudyofthesubgroupgrowthofin?nitegroupsisanareaofmathematical research that has grown rapidly since its inception at the Groups St. Andrews conferencein1985.Ithasbecomearichtheoryrequiringtoolsfromandhaving applications to many areas of group theory. Indeed, much of this progress is chronicled by Lubotzky and Segal within their book [42]. However, one area within this study has grown explosively in the last few years. This is the study of the zeta functions of groups with polynomial s- groupgrowth,inparticularfortorsion-free?nitely-generatednilpotentgroups. These zeta functions were introduced in [32], and other key papers in the - velopment of this subject include [10, 17], with [19, 23, 15] as well as [42] presenting surveys of the area. The purpose of this book is to bring into print signi?cant and as yet unpublished work from three areas of the theory of zeta functions of groups. First, there are now numerous calculations of zeta functions of groups by doctoralstudentsofthe?rstauthorwhichareyettobemadeintoprintedform outside their theses. These explicit calculations provide evidence in favour of conjectures, or indeed can form inspiration and evidence for new conjectures. We record these zeta functions in Chap.2. In particular, we document the functional equations frequently satis?ed by the local factors. Explaining this phenomenon is, according to the ?rst author and Segal [23], “one of the most intriguing open problems in the area”.

Quaternion Algebras

Quaternion Algebras Book
Author : John Voight
Publisher : Springer Nature
Release : 2021-06-28
ISBN : 3030566943
Language : En, Es, Fr & De

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Book Description :

This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.

Cohomological Theory of Dynamical Zeta Functions

Cohomological Theory of Dynamical Zeta Functions Book
Author : Andreas Juhl
Publisher : Birkhäuser
Release : 2012-12-06
ISBN : 3034883404
Language : En, Es, Fr & De

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Book Description :

Dynamical zeta functions are associated to dynamical systems with a countable set of periodic orbits. The dynamical zeta functions of the geodesic flow of lo cally symmetric spaces of rank one are known also as the generalized Selberg zeta functions. The present book is concerned with these zeta functions from a cohomological point of view. Originally, the Selberg zeta function appeared in the spectral theory of automorphic forms and were suggested by an analogy between Weil's explicit formula for the Riemann zeta function and Selberg's trace formula ([261]). The purpose of the cohomological theory is to understand the analytical properties of the zeta functions on the basis of suitable analogs of the Lefschetz fixed point formula in which periodic orbits of the geodesic flow take the place of fixed points. This approach is parallel to Weil's idea to analyze the zeta functions of pro jective algebraic varieties over finite fields on the basis of suitable versions of the Lefschetz fixed point formula. The Lefschetz formula formalism shows that the divisors of the rational Hassc-Wcil zeta functions are determined by the spectra of Frobenius operators on l-adic cohomology.

The Riemann Zeta Function

The Riemann Zeta Function Book
Author : Anatoly A. Karatsuba,S. M. Voronin
Publisher : Walter de Gruyter
Release : 1992-01-01
ISBN : 3110886146
Language : En, Es, Fr & De

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Book Description :

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

p adic Numbers p adic Analysis and Zeta Functions

p adic Numbers  p adic Analysis  and Zeta Functions Book
Author : Neal Koblitz
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461211123
Language : En, Es, Fr & De

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Book Description :

The first edition of this work has become the standard introduction to the theory of p-adic numbers at both the advanced undergraduate and beginning graduate level. This second edition includes a deeper treatment of p-adic functions in Ch. 4 to include the Iwasawa logarithm and the p-adic gamma-function, the rearrangement and addition of some exercises, the inclusion of an extensive appendix of answers and hints to the exercises, as well as numerous clarifications.

Automorphic Forms and Zeta Functions

Automorphic Forms and Zeta Functions Book
Author : Anonim
Publisher : Unknown
Release : 2022-08-17
ISBN : 9814478776
Language : En, Es, Fr & De

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Book Description :

Download Automorphic Forms and Zeta Functions book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Introduction to p adic Analytic Number Theory

Introduction to  p  adic Analytic Number Theory Book
Author : M. Ram Murty
Publisher : American Mathematical Soc.
Release : 2009-02-09
ISBN : 0821847740
Language : En, Es, Fr & De

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Book Description :

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.

Journal of Nonlinear Mathematical Physics Vol 14

Journal of Nonlinear Mathematical Physics Vol  14 Book
Author : Anonim
Publisher : atlantis press
Release : 2022-08-17
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Journal of Nonlinear Mathematical Physics Vol 14 book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Dynamical Spectral and Arithmetic Zeta Functions

Dynamical  Spectral  and Arithmetic Zeta Functions Book
Author : Spectral AMS Special Session on Dynamical,Michel Laurent Lapidus,Machiel Van Frankenhuysen
Publisher : American Mathematical Soc.
Release : 2001
ISBN : 0821820796
Language : En, Es, Fr & De

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Book Description :

The original zeta function was studied by Riemann as part of his investigation of the distribution of prime numbers. Other sorts of zeta functions were defined for number-theoretic purposes, such as the study of primes in arithmetic progressions. This led to the development of $L$-functions, which now have several guises. It eventually became clear that the basic construction used for number-theoretic zeta functions can also be used in other settings, such as dynamics, geometry, and spectral theory, with remarkable results. This volume grew out of the special session on dynamical, spectral, and arithmetic zeta functions held at the annual meeting of the American Mathematical Society in San Antonio, but also includes four articles that were invited to be part of the collection.The purpose of the meeting was to bring together leading researchers, to find links and analogies between their fields, and to explore new methods. The papers discuss dynamical systems, spectral geometry on hyperbolic manifolds, trace formulas in geometry and in arithmetic, as well as computational work on the Riemann zeta function. Each article employs techniques of zeta functions. The book unifies the application of these techniques in spectral geometry, fractal geometry, and number theory. It is a comprehensive volume, offering up-to-date research. It should be useful to both graduate students and confirmed researchers.