The Lerch Zeta Function
DOWNLOAD
Download The Lerch Zeta Function PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get The Lerch Zeta Function 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
The Lerch Zeta Function
DOWNLOAD
Author : Antanas Laurincikas
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
The Lerch Zeta Function written by Antanas Laurincikas 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 2013-12-11 with Mathematics categories.
The Lerch zeta-function is the first monograph on this topic, which is a generalization of the classic Riemann, and Hurwitz zeta-functions. Although analytic results have been presented previously in various monographs on zeta-functions, this is the first book containing both analytic and probability theory of Lerch zeta-functions. The book starts with classical analytical theory (Euler gamma-functions, functional equation, mean square). The majority of the presented results are new: on approximate functional equations and its applications and on zero distribution (zero-free regions, number of nontrivial zeros etc). Special attention is given to limit theorems in the sense of the weak convergence of probability measures for the Lerch zeta-function. From limit theorems in the space of analytic functions the universitality and functional independence is derived. In this respect the book continues the research of the first author presented in the monograph Limit Theorems for the Riemann zeta-function. This book will be useful to researchers and graduate students working in analytic and probabilistic number theory, and can also be used as a textbook for postgraduate students.
Theory Of The Hurwitz Zeta Function Of The Second Variable
DOWNLOAD
Author : Vivek V. Rane
language : en
Publisher:
Release Date : 2015
Theory Of The Hurwitz Zeta Function Of The Second Variable written by Vivek V. Rane and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
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
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.
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
Selberg Zeta Functions And Transfer Operators
DOWNLOAD
Author : Markus Szymon Fraczek
language : en
Publisher: Springer
Release Date : 2017-05-11
Selberg Zeta Functions And Transfer Operators written by Markus Szymon Fraczek and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-11 with Mathematics categories.
This book presents a method for evaluating Selberg zeta functions via transfer operators for the full modular group and its congruence subgroups with characters. Studying zeros of Selberg zeta functions for character deformations allows us to access the discrete spectra and resonances of hyperbolic Laplacians under both singular and non-singular perturbations. Areas in which the theory has not yet been sufficiently developed, such as the spectral theory of transfer operators or the singular perturbation theory of hyperbolic Laplacians, will profit from the numerical experiments discussed in this book. Detailed descriptions of numerical approaches to the spectra and eigenfunctions of transfer operators and to computations of Selberg zeta functions will be of value to researchers active in analysis, while those researchers focusing more on numerical aspects will benefit from discussions of the analytic theory, in particular those concerning the transfer operator method and the spectral theory of hyperbolic spaces.
The Riemann Zeta Function
DOWNLOAD
Author : Anatoly A. Karatsuba
language : en
Publisher: Walter de Gruyter
Release Date : 2011-05-03
The Riemann Zeta Function written by Anatoly A. Karatsuba and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-03 with Mathematics categories.
No detailed description available for "The Riemann Zeta-Function".
Number Theory And Discrete Mathematics
DOWNLOAD
Author : A.K. Agarwal
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Number Theory And Discrete Mathematics written by A.K. Agarwal and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
To mark the World Mathematical Year 2000 an International Conference on Number Theory and Discrete Mathematics in honour of the legendary Indian Mathematician Srinivasa Ramanuj~ was held at the centre for Advanced study in Mathematics, Panjab University, Chandigarh, India during October 2-6, 2000. This volume contains the proceedings of that conference. In all there were 82 participants including 14 overseas participants from Austria, France, Hungary, Italy, Japan, Korea, Singapore and the USA. The conference was inaugurated by Prof. K. N. Pathak, Hon. Vice-Chancellor, Panjab University, Chandigarh on October 2, 2000. Prof. Bruce C. Berndt of the University of Illinois, Urbana Chaimpaign, USA delivered the key note address entitled "The Life, Notebooks and Mathematical Contributions of Srinivasa Ramanujan". He described Ramanujan--as one of this century's most influential Mathematicians. Quoting Mark K. ac, Prof. George E. Andrews of the Pennsylvania State University, USA, in his message for the conference, described Ramanujan as a "magical genius". During the 5-day deliberations invited speakers gave talks on various topics in number theory and discrete mathematics. We mention here a few of them just as a sampling: • M. Waldschmidt, in his article, provides a very nice introduction to the topic of multiple poly logarithms and their special values. • C.
The Riemann Zeta Function
DOWNLOAD
Author : Aleksandar Ivic
language : en
Publisher: Courier Corporation
Release Date : 2012-07-12
The Riemann Zeta Function written by Aleksandar Ivic and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-12 with Mathematics categories.
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.
Value Distribution Of L Functions
DOWNLOAD
Author : Jr̲n Steuding
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-06
Value Distribution Of L Functions written by Jr̲n Steuding 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 2007-06-06 with Mathematics categories.
These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. Universality has a strong impact on the zero-distribution: Riemann’s hypothesis is true only if the Riemann zeta-function can approximate itself uniformly. The text proves universality for polynomial Euler products. The authors’ approach follows mainly Bagchi's probabilistic method. Discussion touches on related topics: almost periodicity, density estimates, Nevanlinna theory, and functional independence.