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Article Dans Une Revue Applicable Analysis and Discrete Mathematics Année : 2022

The extended Eulerian numbers over function fields

Résumé

In this article, we introduce the extended Eulerian numbers for a large class of zeta functions, which includes the zeta functions associated to function fields, and to schemes over finite fields. This construction generalizes the extended Eulerian numbers defined by Carlitz. We give an asymptotic expansion for the summatory function associated to these numbers. Our main result generalizes the well known result on the asymptotic behavior of the extended Eulerian numbers associated to the Riemann zeta function.

Dates et versions

hal-04458844 , version 1 (15-02-2024)

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Citer

Abdelmejid Bayad, Mounir Hajli. The extended Eulerian numbers over function fields. Applicable Analysis and Discrete Mathematics, 2022, 16 (2), pp.508-523. ⟨10.2298/AADM210930019B⟩. ⟨hal-04458844⟩
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