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Article Dans Une Revue Journal of Number Theory Année : 2019

On twisted A-harmonic sums and Carlitz finite zeta values

Résumé

In this paper, we study various twisted A-harmonic sums, named following the seminal log-algebraicity papers of G. Anderson. These objects are partial sums of new types of special zeta values introduced by the first author and linked to certain rank one Drinfeld modules over Tate algebras in positive characteristic by Anglès, Tavares Ribeiro and the first author. We prove that various infinite families of such sums may be interpolated by polynomials, and we deduce, among several other results, properties of analogues of finite zeta values but inside the framework of the Carlitz module. In the theory of finite multi-zeta values as studied by several authors, including Kaneko, Kontsevich, Hoffman, Ohno, Zagier, Zhao et al. finite zeta values are all zero. In the Carlitzian setting, there exist non-vanishing finite zeta values, and we study some of their properties in the present paper.

Dates et versions

hal-01263136 , version 1 (27-01-2016)

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Federico Pellarin, Rudolph Perkins. On twisted A-harmonic sums and Carlitz finite zeta values. Journal of Number Theory, In press, ⟨10.1016/j.jnt.2018.10.018⟩. ⟨hal-01263136⟩
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