Zeta functions for the Riemann zeros
Annales de l'Institut Fourier, Volume 53 (2003) no. 3, p. 665-699
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.
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).
DOI : https://doi.org/10.5802/aif.1955
Classification:  11Mxx,  30B40,  30B50
Keywords: Riemann Zeta function, Riemann zeros, Dirichlet series, Hadamard factorization, meromorphic functions, Mellin transform
@article{AIF_2003__53_3_665_0,
     author = {Voros, Andr\'e},
     title = {Zeta functions for the Riemann zeros},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {53},
     number = {3},
     year = {2003},
     pages = {665-699},
     doi = {10.5802/aif.1955},
     mrnumber = {2008436},
     zbl = {01940707},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2003__53_3_665_0}
}
Zeta functions for the Riemann zeros. Annales de l'Institut Fourier, Volume 53 (2003) no. 3, pp. 665-699. doi : 10.5802/aif.1955. https://aif.centre-mersenne.org/item/AIF_2003__53_3_665_0/

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