no. 3
Zeta functions for the Riemann zeros
[Fonctions Zêta pour les zéros de Riemann]
Voros, André1
1 CEA, Service de Physique Théorique de Saclay, CNRS URA 2306, 91191 Gif-sur-Yvette Cedex (France)
Annales de l'Institut Fourier, Tome 53 (2003) no. 3, pp. 665-699.
corrigé par Erratum - Zeta functions for the Riemann zeros
[Erratum - Fonctions Zêta pour les zéros de Riemann]

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.

DOI : 10.5802/aif.1955
Classification : 11Mxx, 30B40, 30B50
Keywords: Riemann Zeta function, Riemann zeros, Dirichlet series, Hadamard factorization, meromorphic functions, Mellin transform
Mot clés : fonction Zêta de Riemann, zéros de Riemann, séries de Dirichlet, factorisation de Hadamard, fonctions méromorphes, transformation de Mellin

Voros, André 1

1 CEA, Service de Physique Théorique de Saclay, CNRS URA 2306, 91191 Gif-sur-Yvette Cedex (France) 
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.1955/

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