{"paper":{"title":"On the distribution of the rational points on cyclic covers in the absence of roots of unity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Lior Bary-Soroker, Patrick Meisner","submitted_at":"2017-11-13T16:27:31Z","abstract_excerpt":"In this paper we study the number of rational points on curves in an ensemble of abelian covers of the projective line: Let $\\ell$ be a prime, $q$ a prime power and consider the ensemble $\\mathcal{H}_{g,\\ell}$ of $\\ell$-cyclic covers of $\\mathbb{P}^1_{\\mathbb{F}_q}$ of genus $g$.\n  We assume that $q\\not\\equiv 0,1\\mod \\ell$. If $2g+2\\ell-2\\not\\equiv0\\mod (\\ell-1){\\rm ord}_\\ell(q)$, then $\\mathcal{H}_{g,\\ell}$ is empty. Otherwise, the number of rational points on a random curve in $\\mathcal{H}_{g,\\ell}$ distributes as $\\sum_{i=1}^{q+1} X_i$ as $g\\to \\infty$, where $X_1,\\ldots, X_{q+1}$ are i.i.d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04684","kind":"arxiv","version":2},"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"}