{"paper":{"title":"Number of Points on the Full Moduli Space of Curves over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Patrick Meisner","submitted_at":"2016-12-13T13:04:55Z","abstract_excerpt":"The distribution of the number of points on abelian covers of $\\mathbb{P}1(\\mathbb{F}_q)$ 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04137","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}