{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1994:K7NTROBW7YV5LCBS7YH24WBWQP","short_pith_number":"pith:K7NTROBW","schema_version":"1.0","canonical_sha256":"57db38b836fe2bd58832fe0fae583683da4b8bcc8038e739882f62cef6021a88","source":{"kind":"arxiv","id":"math/9408212","version":1},"attestation_state":"computed","paper":{"title":"On the convergence of the zeta function for certain prehomogeneous vector spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Akihiko Yukie","submitted_at":"1994-08-15T00:00:00Z","abstract_excerpt":"Let (G,V) be an irreducible prehomogeneous vector space defined over a number field k, P in k[V] a relative invariant polynomial, and X a rational character of G such that P(gx)=X(g)P(x). Let V_k^{ss}={x \\in V_k such that P(x) is not equal to 0}. For x in V_k^{ss}, let G_x be the stabilizer of x, and G_x^0 the connected component of 1 of G_x. We define L_0 to be the set of x in V_k^{ss} such that G_x^0 does not have a non-trivial rational character. We study the zeta function for (G,V)."},"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":"math/9408212","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"1994-08-15T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"3edc206c455fad31e528c8486458f6d29e9cf1c78092a5ffdb2db3f2a8e8c677","abstract_canon_sha256":"22f6925990f79485ce6d8f7fbbef654b540601d93ca807b1c7f1d9e54f37d00d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:51.170908Z","signature_b64":"hY1IwfbwyTplqNRtJ69qjfpAbS4gsWgFbFysGXkQ2JFZS2WrWBw1889cjEV3O05BTGeeDuuc0t5f6aVAPZfkDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57db38b836fe2bd58832fe0fae583683da4b8bcc8038e739882f62cef6021a88","last_reissued_at":"2026-05-18T01:05:51.170413Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:51.170413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the convergence of the zeta function for certain prehomogeneous vector spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Akihiko Yukie","submitted_at":"1994-08-15T00:00:00Z","abstract_excerpt":"Let (G,V) be an irreducible prehomogeneous vector space defined over a number field k, P in k[V] a relative invariant polynomial, and X a rational character of G such that P(gx)=X(g)P(x). Let V_k^{ss}={x \\in V_k such that P(x) is not equal to 0}. For x in V_k^{ss}, let G_x be the stabilizer of x, and G_x^0 the connected component of 1 of G_x. We define L_0 to be the set of x in V_k^{ss} such that G_x^0 does not have a non-trivial rational character. We study the zeta function for (G,V)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9408212","kind":"arxiv","version":1},"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":"math/9408212","created_at":"2026-05-18T01:05:51.170493+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9408212v1","created_at":"2026-05-18T01:05:51.170493+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9408212","created_at":"2026-05-18T01:05:51.170493+00:00"},{"alias_kind":"pith_short_12","alias_value":"K7NTROBW7YV5","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"K7NTROBW7YV5LCBS","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"K7NTROBW","created_at":"2026-05-18T12:25:47.102015+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/K7NTROBW7YV5LCBS7YH24WBWQP","json":"https://pith.science/pith/K7NTROBW7YV5LCBS7YH24WBWQP.json","graph_json":"https://pith.science/api/pith-number/K7NTROBW7YV5LCBS7YH24WBWQP/graph.json","events_json":"https://pith.science/api/pith-number/K7NTROBW7YV5LCBS7YH24WBWQP/events.json","paper":"https://pith.science/paper/K7NTROBW"},"agent_actions":{"view_html":"https://pith.science/pith/K7NTROBW7YV5LCBS7YH24WBWQP","download_json":"https://pith.science/pith/K7NTROBW7YV5LCBS7YH24WBWQP.json","view_paper":"https://pith.science/paper/K7NTROBW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9408212&json=true","fetch_graph":"https://pith.science/api/pith-number/K7NTROBW7YV5LCBS7YH24WBWQP/graph.json","fetch_events":"https://pith.science/api/pith-number/K7NTROBW7YV5LCBS7YH24WBWQP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K7NTROBW7YV5LCBS7YH24WBWQP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K7NTROBW7YV5LCBS7YH24WBWQP/action/storage_attestation","attest_author":"https://pith.science/pith/K7NTROBW7YV5LCBS7YH24WBWQP/action/author_attestation","sign_citation":"https://pith.science/pith/K7NTROBW7YV5LCBS7YH24WBWQP/action/citation_signature","submit_replication":"https://pith.science/pith/K7NTROBW7YV5LCBS7YH24WBWQP/action/replication_record"}},"created_at":"2026-05-18T01:05:51.170493+00:00","updated_at":"2026-05-18T01:05:51.170493+00:00"}