ゼータ関数の理論 Contributions to the Theory of Zeta-functions: The Modular Relation Supremacy (Series on Number Theory and Its Applications)

Kanemitsu, Shigeru/ Tsukada, Haruo

World Scientific Publishing Co Pte Ltd（2015/02発売）

• 製本 Hardcover:ハードカバー版／ページ数 316 p.
• 言語 ENG
• 商品コード 9789814449618
• DDC分類 515.75

Full 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.

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 ΓΓ-Type; The General Modular Relation of ΓN-Type; The General Modular Relation for Maass Forms.