Number of Points on the Full Moduli Space of Curves over Finite Fields

2016/12/13 by Patrick Meisner, Meisner, Patrick
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1612.04137

openalex publication_date 2016/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The distribution of the number of points on abelian covers of ℙ1(\mathbbF_q) ranging over an irreducible moduli space has been answered in recent work by the author. Bucur, et al. determined the distribution over the whole moduli space for curves with Gal(K(C)/K) a prime cyclic. In this paper, we prove a result towards determining the distribution over the whole moduli space of curves with Gal(K(C)/K) any abelian group. We successfully determine the distribution in the case Gal(K(C)/K) is a power of a prime cyclic.

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