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Article Dans Une Revue International Journal of Number Theory Année : 2013

Generalization of the effective Wiener-Ikehara theorem

Anne de Roton
Szilard Révész
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Résumé

We consider the classical Wiener–Ikehara Tauberian theorem, with a generalized condition of slow decrease and some additional poles on the boundary of convergence of the Laplace transform. In this generality, we prove the otherwise known asymptotic evaluation of the transformed function, when the usual conditions of the Wiener-Ikehara theorem hold. However, our version also provides an effective error term, not known thus far in this generality. The crux of the proof is a proper asymptotic variation of the lemmas of Ganelius and Tenenbaum, also constructed for the sake of an effective version of the Wiener–Ikehara theorem.
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Dates et versions

hal-01096381 , version 1 (23-02-2016)

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Anne de Roton, Szilard Révész. Generalization of the effective Wiener-Ikehara theorem. International Journal of Number Theory, 2013, 9 (8), pp.2091 - 2128. ⟨10.1142/S1793042113500760⟩. ⟨hal-01096381⟩
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