Contributions to the theory of zeta-functions : the modular relation supremacy

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Contributions to the theory of zeta-functions : the modular relation supremacy

Shigeru Kanemitsu and Haruo Tsukada

（Series on number theory and its applications / series editor, Shigeru Kanemitsu, v. 10）

World Scientific, c2015

  • : hardcover

Available at  / 10 libraries

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Includes bibliographical references and index

Description and Table of Contents

Description

This volume provides a systematic survey of almost all the equivalent assertions to the functional equations - zeta symmetry - which zeta-functions satisfy, thus streamlining previously published results on zeta-functions. The equivalent relations are given in the form of modular relations in Fox H-function series, which at present include all that have been considered as candidates for ingredients of a series. The results are presented in a clear and simple manner for readers to readily apply without much knowledge of zeta-functions.This volume aims to keep a record of the 150-year-old heritage starting from Riemann on zeta-functions, which are ubiquitous in all mathematical sciences, wherever there is a notion of the norm. It provides almost all possible equivalent relations to the zeta-functions without requiring a reader's deep knowledge on their definitions. This can be an ideal reference book for those studying zeta-functions.

Table of Contents

  • Introduction and Zeta-Functions
  • G-, H- and Allied Special Functions
  • The General Modular Relation
  • The Fourier - Bessel Expansion
  • The Ewald Expansion
  • The General Modular Relation for Epstein Zeta-Funcion
  • The General Modular Relation of Hecke's Type
  • The General Modular Relation for the Riemann Zeta-Function
  • The General Modular Relation of -Type
  • The General Modular Relation of N-Type
  • The General Modular Relation for Maass Forms.

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