{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2Y6FCK37WL2G44KL6TI3J4TK6A","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"be64a6fabd8731b9b273342bc75c31739db4ad034998b3abd9655b35f9cc183a","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-11-15T17:10:53Z","title_canon_sha256":"d21cb748c0aa5f0ae72f04eea473d2a28246529d8091afa5dae09a142f70358c"},"schema_version":"1.0","source":{"id":"1211.3661","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.3661","created_at":"2026-05-18T03:40:39Z"},{"alias_kind":"arxiv_version","alias_value":"1211.3661v1","created_at":"2026-05-18T03:40:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3661","created_at":"2026-05-18T03:40:39Z"},{"alias_kind":"pith_short_12","alias_value":"2Y6FCK37WL2G","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2Y6FCK37WL2G44KL","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2Y6FCK37","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:0c75506da5e95d12772a966fb445d68e25550a7afcdaca528f9229c54d64cb5b","target":"graph","created_at":"2026-05-18T03:40:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this note, we give a formula for the Whittaker-Shintani functions for the p-adic symplectic groups, which is a generalization of the Zonal spherical functions and Whittaker functions. We then use the formula to give an alternative proof of a conjecture given by T.Shintani on the unramified calculation of L-function for $Sp_{2n}\\times GL_{1}$.","authors_text":"Xin Shen","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-11-15T17:10:53Z","title":"The Whittaker-Shintani functions for symplectic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3661","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:78b9c6753179948093aa155b594c160a0499befdbdb0213304f3d1c9295d6426","target":"record","created_at":"2026-05-18T03:40:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"be64a6fabd8731b9b273342bc75c31739db4ad034998b3abd9655b35f9cc183a","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-11-15T17:10:53Z","title_canon_sha256":"d21cb748c0aa5f0ae72f04eea473d2a28246529d8091afa5dae09a142f70358c"},"schema_version":"1.0","source":{"id":"1211.3661","kind":"arxiv","version":1}},"canonical_sha256":"d63c512b7fb2f46e714bf4d1b4f26af010d1340c5bd632b2589fddb3e6a958d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d63c512b7fb2f46e714bf4d1b4f26af010d1340c5bd632b2589fddb3e6a958d2","first_computed_at":"2026-05-18T03:40:39.137773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:39.137773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ugz1DpPkBRwgNA0eV40o5DcuMTd1v3m2bpY95y7LVxRQapxpJdUxHwOO7ZW8Q2hub3s82ELSeF07NGwaa/w7AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:39.138391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.3661","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78b9c6753179948093aa155b594c160a0499befdbdb0213304f3d1c9295d6426","sha256:0c75506da5e95d12772a966fb445d68e25550a7afcdaca528f9229c54d64cb5b"],"state_sha256":"e024c68e4be5c14c8a8fe54677ed959ab937fa2fc970d1af38c9b18a089c7065"}