On certain generating functions in positive characteristic

Abstract : We present new methods for the study of a class of generating functions introduced by the second author which carry some formal similarities with the Hurwitz zeta function. We prove functional identities which establish an explicit connection with certain deformations of the Carlitz logarithm introduced by M. Papanikolas and involve the Anderson-Thakur function and the Carlitz exponential function. They collect certain functional identities in families for a new class of L-functions introduced by the first author. This paper also deals with specializations at roots of unity of these generating functions, producing a link with Gauss-Thakur sums.
Type de document :
Pré-publication, Document de travail
18 pages. Refereed version. 2016
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https://hal.archives-ouvertes.fr/hal-01066478
Contributeur : Rudolph Perkins <>
Soumis le : jeudi 14 janvier 2016 - 14:22:16
Dernière modification le : vendredi 26 octobre 2018 - 10:38:43
Document(s) archivé(s) le : samedi 16 avril 2016 - 08:32:13

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  • HAL Id : hal-01066478, version 2
  • ARXIV : 1409.6006

Citation

Federico Pellarin, Rudolph Perkins. On certain generating functions in positive characteristic. 18 pages. Refereed version. 2016. 〈hal-01066478v2〉

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