Equidistribution of Gross points over rational function fields

2019/05/16 by Ahmad El‐Guindy, Riad Masri, El-Guindy, Ahmad +5
Mathematics · #11F41 #11F67 #11G09 #11G18 (Secondary) #11R58 (Primary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1905.07001

openalex publication_date 2019/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove a sparse equidistribution theorem for Gross points over the rational function field \mathbbF_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 Lindelöf-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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