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We prove the following local converse theorem for $\\textrm{U}_{2r+1}$: given two irreducible generic supercuspidal representations $\\pi,\\pi_0$ of $\\textrm{U}_{2r+1}$ with the same central character, if $\\gamma(s,\\pi\\times \\tau,\\psi)=\\gamma(s,\\pi_0\\times \\tau,\\psi)$ for all irreducible generic representation $\\tau$ of $\\textrm{GL}_n(E)$ and for all $n$ with $1\\le n\\le r$, then $\\pi\\cong \\pi_0$. The proof depends on analysis of the local integrals which define local gamma fac"},"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":"1705.09410","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-05-26T02:00:21Z","cross_cats_sorted":[],"title_canon_sha256":"df2eb79f6fe58c0bb14d5c5b162cbc0083171af18dd2209418cb08a04e4a211d","abstract_canon_sha256":"741b1ce688dab0bb15771ca654e92bddff2d4ae77f4789502dc72825b4541cfa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:16.874945Z","signature_b64":"teG+ZFNeT4vMPxfSGGNVnTT6dhy3hkLuB7Y3iZ3DnEPtTRCBlYJsxeGWhYRMrLWjxSgod5BcWtYbE7zmLskoAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"113061ce37025b7183105ee4ec4a1d7ed91a0d54a0dad1c347472cfc5a0d6933","last_reissued_at":"2026-05-18T00:30:16.874383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:16.874383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A local converse theorem for $\\textrm{U}_{2r+1}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Qing Zhang","submitted_at":"2017-05-26T02:00:21Z","abstract_excerpt":"Let $E/F$ be a quadratic extension of $p$-adic fields and $\\textrm{U}_{2r+1}$ be the unitary group associated with $E/F$. We prove the following local converse theorem for $\\textrm{U}_{2r+1}$: given two irreducible generic supercuspidal representations $\\pi,\\pi_0$ of $\\textrm{U}_{2r+1}$ with the same central character, if $\\gamma(s,\\pi\\times \\tau,\\psi)=\\gamma(s,\\pi_0\\times \\tau,\\psi)$ for all irreducible generic representation $\\tau$ of $\\textrm{GL}_n(E)$ and for all $n$ with $1\\le n\\le r$, then $\\pi\\cong \\pi_0$. The proof depends on analysis of the local integrals which define local gamma fac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09410","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1705.09410","created_at":"2026-05-18T00:30:16.874468+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.09410v2","created_at":"2026-05-18T00:30:16.874468+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09410","created_at":"2026-05-18T00:30:16.874468+00:00"},{"alias_kind":"pith_short_12","alias_value":"CEYGDTRXAJNX","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_16","alias_value":"CEYGDTRXAJNXDAYQ","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_8","alias_value":"CEYGDTRX","created_at":"2026-05-18T12:31:10.602751+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CEYGDTRXAJNXDAYQL3SOYSQ5P3","json":"https://pith.science/pith/CEYGDTRXAJNXDAYQL3SOYSQ5P3.json","graph_json":"https://pith.science/api/pith-number/CEYGDTRXAJNXDAYQL3SOYSQ5P3/graph.json","events_json":"https://pith.science/api/pith-number/CEYGDTRXAJNXDAYQL3SOYSQ5P3/events.json","paper":"https://pith.science/paper/CEYGDTRX"},"agent_actions":{"view_html":"https://pith.science/pith/CEYGDTRXAJNXDAYQL3SOYSQ5P3","download_json":"https://pith.science/pith/CEYGDTRXAJNXDAYQL3SOYSQ5P3.json","view_paper":"https://pith.science/paper/CEYGDTRX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.09410&json=true","fetch_graph":"https://pith.science/api/pith-number/CEYGDTRXAJNXDAYQL3SOYSQ5P3/graph.json","fetch_events":"https://pith.science/api/pith-number/CEYGDTRXAJNXDAYQL3SOYSQ5P3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CEYGDTRXAJNXDAYQL3SOYSQ5P3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CEYGDTRXAJNXDAYQL3SOYSQ5P3/action/storage_attestation","attest_author":"https://pith.science/pith/CEYGDTRXAJNXDAYQL3SOYSQ5P3/action/author_attestation","sign_citation":"https://pith.science/pith/CEYGDTRXAJNXDAYQL3SOYSQ5P3/action/citation_signature","submit_replication":"https://pith.science/pith/CEYGDTRXAJNXDAYQL3SOYSQ5P3/action/replication_record"}},"created_at":"2026-05-18T00:30:16.874468+00:00","updated_at":"2026-05-18T00:30:16.874468+00:00"}