{"paper":{"title":"p-adic Gamma function and traces of Frobenius of elliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Neelam Saikia, Rupam Barman","submitted_at":"2013-04-11T14:32:49Z","abstract_excerpt":"In \\cite{mccarthy2}, McCarthy defined a function $_{n}G_{n}[\\cdots]$ using Teichm\\\"{u}ller character of finite fields and quotients of $p$-adic gamma function, and expressed the trace of Frobenius of elliptic curves in terms of special values of $_{2}G_{2}[\\cdots]$. We establish two different expressions for the traces of Frobenius of elliptic curves in terms of the function $_{2}G_{2}[\\cdots]$. As a result, we obtain two relations between special values of the function $_{2}G_{2}[\\cdots]$ with different parameters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3321","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"}