{"paper":{"title":"The distribution of $\\mathbb{F}_q$-points on cyclic $\\ell$-covers of genus $g$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alina Bucur, Brooke Feigon, Chantal David, Ekin Ozman, Matilde Lal\\'in, Melanie Matchett Wood, Nathan Kaplan","submitted_at":"2015-05-26T21:07:43Z","abstract_excerpt":"We study fluctuations in the number of points of $\\ell$-cyclic covers of the projective line over the finite field $\\mathbb{F}_q$ when $q \\equiv 1 \\mod \\ell$ is fixed and the genus tends to infinity. The distribution is given as a sum of $q+1$ i.i.d. random variables. This was settled for hyperelliptic curves by Kurlberg and Rudnick, while statistics were obtained for certain components of the moduli space of $\\ell$-cyclic covers by Bucur, David, Feigon and Lal\\'{i}n. In this paper, we obtain statistics for the distribution of the number of points as the covers vary over the full moduli space "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07136","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"}