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Article Dans Une Revue Acta Arithmetica Année : 2007

On the mean square of the error term for an extended Selberg's class

Anne de Roton

Résumé

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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Dates et versions

hal-00091969 , version 1 (07-09-2006)

Identifiants

Citer

Anne de Roton. On the mean square of the error term for an extended Selberg's class. Acta Arithmetica, 2007, 126 (1), pp.27-55. ⟨10.4064/aa126-1-2⟩. ⟨hal-00091969⟩
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