Contributions to the theory of zeta-functions : the modular relation supremacy
著者
書誌事項
Contributions to the theory of zeta-functions : the modular relation supremacy
（Series on number theory and its applications / series editor, Shigeru Kanemitsu, v. 10）
World Scientific, c2015
- : hardcover
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- 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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