TY  - BOOK
AU  - Kanemitsu,Shigeru
AU  - Tsukada,Haruo
TI  - Contributions to the theory of zeta-functions: the modular relation supremacy 
T2  - Series on number theory and its applications
SN  - 9789814449618 (hardcover : alk. paper)
U1  - 515.56 23
PY  - 2015///
CY  - New Jersey
PB  - World Scientific
KW  - Zeta functions
KW  - Functional equations
KW  - Mathematics
N1  - Includes bibliographical references and index; 1. Prelude --
2. Grocery of special functions --
3. Unprocessed modular reactions --
4. Fourier-Bessel expansion [characters omitted] --
5. The Ewald expansion or the incomplete gamma series --
6. The Riesz sums --
7. The general modular relation --
8. The Hecke type zeta-functions --
9. The product of zeta-functions --
10. Miscellany.
N2  - 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
ER  -