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arXiv · 1905.07001

Equidistribution of Gross points over rational function fields

Ahmad El-Guindy·Riad Masri·Matthew Papanikolas·Guchao Zeng
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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.

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Ahmad El-Guindy, Riad Masri, Matthew Papanikolas, Guchao Zeng. 2019-05-16. Equidistribution of Gross points over rational function fields. https://arxiv.org/abs/1905.07001

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