# Equidistribution of Gross points over rational function fields

## TL;DR

This paper establishes a sparse equidistribution theorem for Gross points over rational function fields and applies it to analyze the reduction map from CM Drinfeld modules to supersingular ones, using advanced automorphic form techniques.

## Contribution

It introduces a new sparse equidistribution result for Gross points over $\,\mathbb{F}_q(t)$ and connects it to the reduction theory of Drinfeld modules.

## Key findings

- Proves a sparse equidistribution theorem for Gross points
- Analyzes the reduction map from CM to supersingular Drinfeld modules
- Utilizes a Lindelöf-type bound for Rankin-Selberg L-values

## Abstract

In this paper we prove a sparse equidistribution theorem for Gross points over the rational function field $\mathbb{F}_q(t)$. We apply this result to study the reduction map from CM Drinfeld modules to supersingular Drinfeld modules. Our proofs rely crucially on a period formula due to M. Papikian and F.-T. Wei/J. Yu, and a Lindel\"of-type bound for central values of Rankin-Selberg $L$-functions associated to twists of automorphic forms of Drinfeld-type by ideal class group characters.