{"paper":{"title":"Statistics for biquadratic covers of the projective line over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alina Bucur, Elisa Lorenzo, Giulio Meleleo, Piermarco Milione","submitted_at":"2015-03-11T11:22:35Z","abstract_excerpt":"We study the distribution of the traces of the Frobenius endomorphism of genus $g$ curves which are quartic non-cyclic covers of $\\mathbb{P}^{1}_{\\mathbb{F}_{q}}$, as the curve varies in an irreducible component of the moduli space. We show that for $q$ fixed, the limiting distribution of the trace of Frobenius equals the sum of $q + 1$ independent random discrete variables. We also show that when both $g$ and $q$ go to infinity, the normalized trace has a standard complex Gaussian distribution. Finally, we extend these computations to the general case of arbitrary covers of $\\mathbb{P}^{1}_{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03276","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"}