{"paper":{"title":"Arithmetic properties of the Frobenius traces defined by a rational abelian variety (with two appendices by J-P. Serre)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alice Silverberg, Alina Carmen Cojocaru, Katherine E. Stange, Rachel Davis","submitted_at":"2015-04-03T17:48:32Z","abstract_excerpt":"Let $A$ be an abelian variety over $\\mathbb{Q}$ of dimension $g$ such that the image of its associated absolute Galois representation $\\rho_A$ is open in $\\operatorname{GSp}_{2g}(\\hat{\\mathbb{Z}})$. We investigate the arithmetic of the traces $a_{1, p}$ of the Frobenius at $p$ in $\\operatorname{Gal}(\\overline{\\mathbb{Q}}/\\mathbb{Q})$ under $\\rho_A$, modulo varying primes $p$. In particular, we obtain upper bounds for the counting function $\\#\\{p \\leq x: a_{1, p} = t\\}$ and we prove an Erd\\\"os-Kac type theorem for the number of prime factors of $a_{1, p}$. We also formulate a conjecture about t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00902","kind":"arxiv","version":4},"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"}