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The Lerch Zeta-function

  • Antanas Laurinčikas
  • Ramūnas Garunkštis

Table of contents

  1. Front Matter
    Pages i-viii
  2. Antanas Laurinčikas, Ramūnas Garunkštis
    Pages 1-15
  3. Antanas Laurinčikas, Ramūnas Garunkštis
    Pages 17-30
  4. Antanas Laurinčikas, Ramūnas Garunkštis
    Pages 31-51
  5. Antanas Laurinčikas, Ramūnas Garunkštis
    Pages 53-69
  6. Antanas Laurinčikas, Ramūnas Garunkštis
    Pages 71-109
  7. Antanas Laurinčikas, Ramūnas Garunkštis
    Pages 111-135
  8. Antanas Laurinčikas, Ramūnas Garunkštis
    Pages 137-142
  9. Antanas Laurinčikas, Ramūnas Garunkštis
    Pages 143-179
  10. Back Matter
    Pages 180-189

About this book

Introduction

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.

Keywords

analytic function approximation distribution functional equation Moment number theory probability probability theory

Authors and affiliations

  • Antanas Laurinčikas
    • 1
    • 2
  • Ramūnas Garunkštis
    • 1
  1. 1.Vilnius UniversityVilniusLithuania
  2. 2.Šiauliai UniversityŠiauliaiLithuania

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-6401-8
  • Copyright Information Springer Science+Business Media B.V. 2002
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-6168-3
  • Online ISBN 978-94-017-6401-8
  • Buy this book on publisher's site