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Pré-Publication, Document De Travail Année : 2016

On certain generating functions in positive characteristic

Federico Pellarin

Résumé

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.
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Dates et versions

hal-01066478 , version 1 (20-09-2014)
hal-01066478 , version 2 (14-01-2016)

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Federico Pellarin, Rudolph Perkins. On certain generating functions in positive characteristic. 2016. ⟨hal-01066478v2⟩
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