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Contributions to the theory of zeta-functions : the modular relation supremacy / Shigeru Kanemitsu and Haruo Tsukada.

By: Contributor(s): Material type: TextTextSeries: Series on number theory and its applications ; v 10.Publication details: New Jersey : World Scientific, ©2015.Description: xii, 303 pages : illustrations ; 25 cmISBN:
  • 9789814449618 (hardcover : alk. paper)
Subject(s): DDC classification:
  • 515.56 23 K16
Contents:
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.
Summary: 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.
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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.

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.

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