Certaines fonctions Zêta définies sur les zéros de Riemann, par une famille de séries de Dirichlet, se prolongent à tout le plan complexe en des fonctions méromorphes, dont de nombreuses caractéristiques peuvent être explicitées (la structure polaire, mais aussi une infinité de valeurs spéciales).
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.
Classification : 11Mxx, 30B40, 30B50
Mots clés : fonction Zêta de Riemann, zéros de Riemann, séries de Dirichlet, factorisation de Hadamard, fonctions méromorphes, transformation de Mellin
@article{AIF_2003__53_3_665_0,
author = {Voros, Andr\'e},
title = {Zeta functions for the Riemann zeros},
journal = {Annales de l'Institut Fourier},
pages = {665--699},
publisher = {Association des Annales de l'institut Fourier},
volume = {53},
number = {3},
year = {2003},
doi = {10.5802/aif.1955},
zbl = {01940707},
mrnumber = {2008436},
language = {en},
url = {archive.numdam.org/item/AIF_2003__53_3_665_0/}
}
Voros, André. Zeta functions for the Riemann zeros. Annales de l'Institut Fourier, Tome 53 (2003) no. 3, pp. 665-699. doi : 10.5802/aif.1955. http://archive.numdam.org/item/AIF_2003__53_3_665_0/
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