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| HAL : hal-00091969, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Acta Arithmetica 126, 1 (2007) 27-55 |
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| On the mean square of the error term for an extended Selberg's class |
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| Anne De Roton 1 |
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| (2007) |
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| We are concerned with an estimate and a mean square theorem for the summatory function of a class of Dirichlet series. This extension of Selberg's class is a class of Dirichlet series satisfying a functional equation involving multiple gamma factors and, contrary to the class studied by Chandrasekharan and Narasimhan, a conjugate, which allows twisted functions to belong to this class. If $F(s)=\sum_{n=1}^{+\infty}a_{n}n^{-s}$ is a Dirichlet series satisfying such a functional equation and $E(x)$ is the associated error term, then we prove $O$-estimate for $E(x)$ and $\int_{0}^{x}|E(y)|^2dy$. These results are similar to those of Chandrasekharan and Narasimhan but are applicable in cases where theirs are not. |
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| 1 : | Institut Elie Cartan Nancy (IECN) |
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CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine |
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| Théorie des nombres |
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| Domaine | : | Mathématiques/Théorie des nombres |
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| Dirichlet series – Voronoï's method – hypergeometric functions |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00091969, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00091969 | |
| oai:hal.archives-ouvertes.fr:hal-00091969 | |
| Contributeur : Anne De Roton | |
| Soumis le : Jeudi 7 Septembre 2006, 16:57:19 | |
| Dernière modification le : Mardi 11 Septembre 2007, 14:41:59 | |
