{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:36BEHRE664STEW7YZVSIPYKD6X","short_pith_number":"pith:36BEHRE6","schema_version":"1.0","canonical_sha256":"df8243c49ef725325bf8cd6487e143f5c830a87e094250fce8d4f18671862fbc","source":{"kind":"arxiv","id":"1604.01914","version":2},"attestation_state":"computed","paper":{"title":"Traces des op\\'erateurs de Hecke sur les espaces de formes automorphes de $\\mathrm{SO}_7$, $\\mathrm{SO}_8$ ou $\\mathrm{SO}_9$ en niveau $1$ et poids arbitraire","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Thomas M\\'egarban\\'e","submitted_at":"2016-04-07T08:17:36Z","abstract_excerpt":"In this article, we determine the trace of some Hecke operators on the spaces of level one automorphic forms on the special orthogonal groups of the euclidean lattices $\\mathrm{E}_7$, $\\mathrm{E}_8$ and $\\mathrm{E}_8\\oplus \\mathrm{A}_1$, with arbitrary weight. Using Arthur's theory, we deduce properties of the Satake parameters of the automorphic representations for the linear groups discovered by Chenevier and Renard. Our results corroborate a conjecture by Bergstr\\\"om, Faber and van der Geer about the Hasse-Weil zeta function on the moduli spaces of $17$-pointed curves of genus $3$."},"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":"1604.01914","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-07T08:17:36Z","cross_cats_sorted":[],"title_canon_sha256":"c482eabd867f1ccd22ca2fbfc1ce18b6c67eb71140678a99cf10a87f7dad3020","abstract_canon_sha256":"4ac59f0989018c6accd9ac3079bcbc2bce0c2515a3cdc1b1b20da3a616175067"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:57.308262Z","signature_b64":"LqGTpC052QMS9jNnn8Hf3+nXz7if6gNP+ika+jlLvobopyIgpQnxTbvcq+DhiINvWfENs9PLI8BpXJHXd2SaCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df8243c49ef725325bf8cd6487e143f5c830a87e094250fce8d4f18671862fbc","last_reissued_at":"2026-05-18T01:15:57.307592Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:57.307592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Traces des op\\'erateurs de Hecke sur les espaces de formes automorphes de $\\mathrm{SO}_7$, $\\mathrm{SO}_8$ ou $\\mathrm{SO}_9$ en niveau $1$ et poids arbitraire","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Thomas M\\'egarban\\'e","submitted_at":"2016-04-07T08:17:36Z","abstract_excerpt":"In this article, we determine the trace of some Hecke operators on the spaces of level one automorphic forms on the special orthogonal groups of the euclidean lattices $\\mathrm{E}_7$, $\\mathrm{E}_8$ and $\\mathrm{E}_8\\oplus \\mathrm{A}_1$, with arbitrary weight. Using Arthur's theory, we deduce properties of the Satake parameters of the automorphic representations for the linear groups discovered by Chenevier and Renard. Our results corroborate a conjecture by Bergstr\\\"om, Faber and van der Geer about the Hasse-Weil zeta function on the moduli spaces of $17$-pointed curves of genus $3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01914","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":"1604.01914","created_at":"2026-05-18T01:15:57.307716+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.01914v2","created_at":"2026-05-18T01:15:57.307716+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01914","created_at":"2026-05-18T01:15:57.307716+00:00"},{"alias_kind":"pith_short_12","alias_value":"36BEHRE664ST","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"36BEHRE664STEW7Y","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"36BEHRE6","created_at":"2026-05-18T12:29:55.572404+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/36BEHRE664STEW7YZVSIPYKD6X","json":"https://pith.science/pith/36BEHRE664STEW7YZVSIPYKD6X.json","graph_json":"https://pith.science/api/pith-number/36BEHRE664STEW7YZVSIPYKD6X/graph.json","events_json":"https://pith.science/api/pith-number/36BEHRE664STEW7YZVSIPYKD6X/events.json","paper":"https://pith.science/paper/36BEHRE6"},"agent_actions":{"view_html":"https://pith.science/pith/36BEHRE664STEW7YZVSIPYKD6X","download_json":"https://pith.science/pith/36BEHRE664STEW7YZVSIPYKD6X.json","view_paper":"https://pith.science/paper/36BEHRE6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.01914&json=true","fetch_graph":"https://pith.science/api/pith-number/36BEHRE664STEW7YZVSIPYKD6X/graph.json","fetch_events":"https://pith.science/api/pith-number/36BEHRE664STEW7YZVSIPYKD6X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/36BEHRE664STEW7YZVSIPYKD6X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/36BEHRE664STEW7YZVSIPYKD6X/action/storage_attestation","attest_author":"https://pith.science/pith/36BEHRE664STEW7YZVSIPYKD6X/action/author_attestation","sign_citation":"https://pith.science/pith/36BEHRE664STEW7YZVSIPYKD6X/action/citation_signature","submit_replication":"https://pith.science/pith/36BEHRE664STEW7YZVSIPYKD6X/action/replication_record"}},"created_at":"2026-05-18T01:15:57.307716+00:00","updated_at":"2026-05-18T01:15:57.307716+00:00"}