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.
Document type :
Preprints, Working Papers, ...
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01066478
Contributor : Rudolph Perkins <>
Submitted on : Thursday, January 14, 2016 - 2:22:16 PM
Last modification on : Friday, October 26, 2018 - 10:38:43 AM
Document(s) archivé(s) le : Saturday, April 16, 2016 - 8:32:13 AM

Files

CGFarxivfinal.pdf
Files produced by the author(s)

Identifiers

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

Citation

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

Share

Metrics

Record views

302

Files downloads

80