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arXiv · 2209.05576

Counting Drinfeld modules with prescribed local conditions

Tristan Phillips
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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.

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Tristan Phillips. 2022-09-12. Counting Drinfeld modules with prescribed local conditions. https://doi.org/10.1007/s40993-023-00500-7

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