Séminaire Combinatoire et Théorie des Nombres ICJ

Taylor coefficients of Anderson generating functions

by Andreas Maurischat (RWTH Aachen University)

Europe/Paris
Bât. Braconnier, salle Fokko du Cloux (ICJ, Université Lyon 1)

Bât. Braconnier, salle Fokko du Cloux

ICJ, Université Lyon 1

Description

Algebraic extensions of the rational function field $K=\mathbb{F}_q(\theta)$ can be obtained by adjoining torsion points of Drinfeld modules over $K$. The Anderson generating functions for such Drinfeld modules are defined as certain power series $\sum c_it^i \in \bar{K}[[t]]$ which converge for all $|t| \leq 1$ with respect to (an extension of) the norm associated to the infinite place of $K$. In particular, they converge at all roots of unity.
After an introduction to the subject, the main goal of this talk is to explain how the coefficients of the Taylor expansions of the Anderson generating functions at roots of unity give rise to prime power torsion points of the Drinfeld module. This is joint work with Rudy Perkins.