On the generalized Carlitz module

Abstract

The aim of this note is to gather formal similarities between two apparently different functions; {\em Euler's function} $\Gamma$ and {\em Anderson-Thakur function} $\omega$. We discuss these similarities in the framework of the {\em generalized Carlitz's module}, a common structure which can be helpful in framing the theories of both functions. We further analyze several noticeable differences while investigating the {\em exponential functions} associated to these structures.

References in corpus (1)

• Values of certain L-series in positive characteristic

Cited by in corpus (3)

• An exact degree for multivariate special polynomials
• Polynomial-exponential equations -- some new cases of solvability
• The analytic theory of vectorial Drinfeld modular forms