{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:6LTH575FOR4V4DOPSSVHNSASIT","short_pith_number":"pith:6LTH575F","schema_version":"1.0","canonical_sha256":"f2e67effa574795e0dcf94aa76c81244d50f9638d3e16575a41273f08dbe8a27","source":{"kind":"arxiv","id":"1303.0889","version":3},"attestation_state":"computed","paper":{"title":"Weighted Sato-Tate Vertical Distribution of the Satake Parameter of Maass Forms on PGL(N)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fan Zhou","submitted_at":"2013-03-04T23:15:53Z","abstract_excerpt":"We formulate a conjectured orthogonality relation between the Fourier coefficients of Maass forms on PGL(N) for N>=2. Based on the work of Goldfeld-Kontorovich and Blomer for N=3, and on our conjecture for N>=4, we prove a weighted vertical equidistribution theorem (with respect to the generalized Sato-Tate measure) for the Satake parameter of Maass forms at a finite prime. For N=3, the rate of convergence for the equidistribution theorem is obtained."},"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":"1303.0889","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-03-04T23:15:53Z","cross_cats_sorted":[],"title_canon_sha256":"756f0eed40c8ee030d4df994b0b2f7431c28f36e6f953a2a813c975e659a6a32","abstract_canon_sha256":"e1aadc508c4487ad4f2e9277abd84ccc9340c84ab4914492878b4df68f8f5a30"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:58.592392Z","signature_b64":"zQQvm47JYaMh9Eg22l3T5z6gxJQDstfahBGgeZQJte4X9XAJg3lkD2VBLbRLZYGWpjsHaJNx277LXEBQd9rCBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2e67effa574795e0dcf94aa76c81244d50f9638d3e16575a41273f08dbe8a27","last_reissued_at":"2026-05-18T00:51:58.591939Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:58.591939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weighted Sato-Tate Vertical Distribution of the Satake Parameter of Maass Forms on PGL(N)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fan Zhou","submitted_at":"2013-03-04T23:15:53Z","abstract_excerpt":"We formulate a conjectured orthogonality relation between the Fourier coefficients of Maass forms on PGL(N) for N>=2. Based on the work of Goldfeld-Kontorovich and Blomer for N=3, and on our conjecture for N>=4, we prove a weighted vertical equidistribution theorem (with respect to the generalized Sato-Tate measure) for the Satake parameter of Maass forms at a finite prime. For N=3, the rate of convergence for the equidistribution theorem is obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0889","kind":"arxiv","version":3},"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":"1303.0889","created_at":"2026-05-18T00:51:58.592010+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.0889v3","created_at":"2026-05-18T00:51:58.592010+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0889","created_at":"2026-05-18T00:51:58.592010+00:00"},{"alias_kind":"pith_short_12","alias_value":"6LTH575FOR4V","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"6LTH575FOR4V4DOP","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"6LTH575F","created_at":"2026-05-18T12:27:36.564083+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/6LTH575FOR4V4DOPSSVHNSASIT","json":"https://pith.science/pith/6LTH575FOR4V4DOPSSVHNSASIT.json","graph_json":"https://pith.science/api/pith-number/6LTH575FOR4V4DOPSSVHNSASIT/graph.json","events_json":"https://pith.science/api/pith-number/6LTH575FOR4V4DOPSSVHNSASIT/events.json","paper":"https://pith.science/paper/6LTH575F"},"agent_actions":{"view_html":"https://pith.science/pith/6LTH575FOR4V4DOPSSVHNSASIT","download_json":"https://pith.science/pith/6LTH575FOR4V4DOPSSVHNSASIT.json","view_paper":"https://pith.science/paper/6LTH575F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.0889&json=true","fetch_graph":"https://pith.science/api/pith-number/6LTH575FOR4V4DOPSSVHNSASIT/graph.json","fetch_events":"https://pith.science/api/pith-number/6LTH575FOR4V4DOPSSVHNSASIT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6LTH575FOR4V4DOPSSVHNSASIT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6LTH575FOR4V4DOPSSVHNSASIT/action/storage_attestation","attest_author":"https://pith.science/pith/6LTH575FOR4V4DOPSSVHNSASIT/action/author_attestation","sign_citation":"https://pith.science/pith/6LTH575FOR4V4DOPSSVHNSASIT/action/citation_signature","submit_replication":"https://pith.science/pith/6LTH575FOR4V4DOPSSVHNSASIT/action/replication_record"}},"created_at":"2026-05-18T00:51:58.592010+00:00","updated_at":"2026-05-18T00:51:58.592010+00:00"}