Contributions to the Theory of Zeta-Functions
The Modular Relation Supremacy
Nonfiction, Science & Nature, Mathematics, Functional Analysis, Number Theory
| Author: | Shigeru Kanemitsu, Haruo Tsukada | ISBN: | 9789814449632 |
| Publisher: | World Scientific Publishing Company | Publication: | December 15, 2014 |
| Imprint: | WSPC | Language: | English |
| Author: | Shigeru Kanemitsu, Haruo Tsukada |
| ISBN: | 9789814449632 |
| Publisher: | World Scientific Publishing Company |
| Publication: | December 15, 2014 |
| Imprint: | WSPC |
| Language: | English |
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:
-
Prelude
-
Grocery of Special Functions
-
Unprocessed Modular Relations
-
Fourier-Bessel Expansion H1;11;1↔ H2;00;2
-
The Ewald Expansion or the Incomplete Gamma Series
-
The Riesz Sums
-
The General Modular Relation
-
The Hecke Type Zeta-functions
-
The Product of Zeta-functions
-
Miscellany
-
Readership:
-
Key Features:
-
The book gives a thorough description of a.a. possible equivalent relations to the functional equation in terms of the H-function series for zeta-functions that have been studied
Given a functional equation, the book immediately informs the reader of the direction to be taken to reach the ultimate aim concerning the zeta-function in both pure and applied disciplines
The reader can forget about the difficult definition of zeta-functions themselves and can refer to the form of functional equation and check how multiple is the gamma factor
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:
-
Prelude
-
Grocery of Special Functions
-
Unprocessed Modular Relations
-
Fourier-Bessel Expansion H1;11;1↔ H2;00;2
-
The Ewald Expansion or the Incomplete Gamma Series
-
The Riesz Sums
-
The General Modular Relation
-
The Hecke Type Zeta-functions
-
The Product of Zeta-functions
-
Miscellany
-
Readership:
-
Key Features:
-
The book gives a thorough description of a.a. possible equivalent relations to the functional equation in terms of the H-function series for zeta-functions that have been studied
Given a functional equation, the book immediately informs the reader of the direction to be taken to reach the ultimate aim concerning the zeta-function in both pure and applied disciplines
The reader can forget about the difficult definition of zeta-functions themselves and can refer to the form of functional equation and check how multiple is the gamma factor
