On certain generating functions in positive characteristic

• Verfasst von: Pellarin, Federico [VerfasserIn]
• Verfasst von: Perkins, Rudolph [VerfasserIn]
• Titel: On certain generating functions in positive characteristic
• Verf.angabe: F. Pellarin, R. B. Perkins
• E-Jahr: 2016
• Jahr: 08 February 2016
• Umfang: 12 S.
• Fussnoten: Gesehen am 16.09.2020 ; Published: 08 February 2016
• Titel Quelle: Enthalten in: Monatshefte für Mathematik
• Ort Quelle: Wien [u.a.] : Springer, 1890
• Jahr Quelle: 2016
• Band/Heft Quelle: 180(2016), 1, Seite 123-144
• ISSN Quelle: 1436-5081
• DOI: doi:10.1007/s00605-016-0880-6
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1733175202

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.