Counting Drinfeld modules with prescribed local conditions

Abstract

We give asymptotics for the number of Drinfeld ${\mathbb{F}}_q[T]$-modules over ${\mathbb{F}}_q(T)$ of a given height, which satisfy prescribed sets of local conditions. This is done by relating our problem to a problem about counting points on weighted projective spaces. Our results for counting points of bounded height on weighted projective spaces over global function fields may be of independent interest.

20 pages. Comments, corrections, questions, and/or suggestions all welcome

Cited by in corpus (1)

• Points of bounded height on weighted projective spaces over global function fields