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＜電子ブック＞
The Lerch zeta-function / by Antanas Laurincikas, Ramunas Garunkstis

版	1st ed. 2002.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	2002
本文言語	英語
大きさ	VIII, 189 p : online resource
著者標目	*Laurincikas, Antanas author Garunkstis, Ramunas author SpringerLink (Online service)
件　名	LCSH:Number theory LCSH:Functions of complex variables LCSH:Special functions LCSH:Probabilities LCSH:Difference equations LCSH:Functional equations FREE:Number Theory FREE:Functions of a Complex Variable FREE:Special Functions FREE:Probability Theory FREE:Difference and Functional Equations
一般注記	Preface -- 1: Euler Gamma-Function -- 2: Functional Equation -- 3: Moments -- 4: Approximate Functional Equation -- 5: Statistical Properties -- 6: Universality -- 7: Functional Independence -- 8: Distribution of Zeros -- References -- Notation -- Subject Index 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 HTTP:URL=https://doi.org/10.1007/978-94-017-6401-8

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