Zeta functions for the Riemann zeros

André Voros[1]

  • [1] CEA, Service de Physique Théorique de Saclay, CNRS URA 2306, 91191 Gif-sur-Yvette Cedex (France)

Annales de l’institut Fourier (2003)

  • Volume: 53, Issue: 3, page 665-699
  • ISSN: 0373-0956

Abstract

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A family of Zeta functions built as Dirichlet series over the Riemann zeros are shown to have meromorphic extensions in the whole complex plane, for which numerous analytical features (the polar structures, plus countably many special values) are explicitly displayed.

How to cite

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Voros, André. "Zeta functions for the Riemann zeros." Annales de l’institut Fourier 53.3 (2003): 665-699. <http://eudml.org/doc/116048>.

@article{Voros2003,
abstract = {A family of Zeta functions built as Dirichlet series over the Riemann zeros are shown to have meromorphic extensions in the whole complex plane, for which numerous analytical features (the polar structures, plus countably many special values) are explicitly displayed.},
affiliation = {CEA, Service de Physique Théorique de Saclay, CNRS URA 2306, 91191 Gif-sur-Yvette Cedex (France)},
author = {Voros, André},
journal = {Annales de l’institut Fourier},
keywords = {Riemann Zeta function; Riemann zeros; Dirichlet series; Hadamard factorization; meromorphic functions; Mellin transform},
language = {eng},
number = {3},
pages = {665-699},
publisher = {Association des Annales de l'Institut Fourier},
title = {Zeta functions for the Riemann zeros},
url = {http://eudml.org/doc/116048},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Voros, André
TI - Zeta functions for the Riemann zeros
JO - Annales de l’institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 3
SP - 665
EP - 699
AB - A family of Zeta functions built as Dirichlet series over the Riemann zeros are shown to have meromorphic extensions in the whole complex plane, for which numerous analytical features (the polar structures, plus countably many special values) are explicitly displayed.
LA - eng
KW - Riemann Zeta function; Riemann zeros; Dirichlet series; Hadamard factorization; meromorphic functions; Mellin transform
UR - http://eudml.org/doc/116048
ER -

References

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Reference updated by author André Voros: [41] M. Hirano, N. Kurokawa, M. Nakayama, Half Zeta functions, J. Ramanujan Math. Soc. v. 18 (2003) 195--209.

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