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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1304.3321","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-04-11T14:32:49Z","cross_cats_sorted":[],"title_canon_sha256":"43e877bd2d8c26284398484319f43f5f3b233297b3545b6d56d4a1949635f301","abstract_canon_sha256":"5e32d6812653a3ff0dc0549dfddb0a3e677105e67b9bf9d8104b2b1fa17a82d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:42.949944Z","signature_b64":"yVbTwv/CML/BtTfD6tDz7dTnEF2Ut1yRVj+Ax346yLYFNFF4fWIJCuyNSLeprwfIv8CeGNMUG8l4Esjprn/uAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07b480eda0386f62adee5182a28b07878863088cbd1e28f326819da257612ef1","last_reissued_at":"2026-05-18T03:06:42.949437Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:42.949437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $_{2}G_{2}[\\cdots]$. 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