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Table of contents (8 chapters)
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: The Lerch zeta-function
Authors: Antanas Laurinčikas, Ramūnas Garunkštis
DOI: https://doi.org/10.1007/978-94-017-6401-8
Publisher: Springer Dordrecht
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media B.V. 2002
Hardcover ISBN: 978-1-4020-1014-9Published: 31 March 2003
Softcover ISBN: 978-90-481-6168-3Published: 04 December 2010
eBook ISBN: 978-94-017-6401-8Published: 11 December 2013
Edition Number: 1
Number of Pages: VIII, 189
Topics: Number Theory, Functions of a Complex Variable, Special Functions, Probability Theory and Stochastic Processes, Difference and Functional Equations