{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:EE2JAT543VBZYZZ6UK2JZNXELZ","short_pith_number":"pith:EE2JAT54","schema_version":"1.0","canonical_sha256":"2134904fbcdd439c673ea2b49cb6e45e4e4fad35fc668b559ec87ec9e23646f0","source":{"kind":"arxiv","id":"0809.1401","version":3},"attestation_state":"computed","paper":{"title":"The Zeta Functions of Complexes from $\\PGL(3)$: a Representation-theoretic Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Chian-Jen Wang, Ming-Hsuan Kang, Wen-Ching Winnie Li","submitted_at":"2008-09-08T18:36:08Z","abstract_excerpt":"The zeta function attached to a finite complex $X_\\Gamma$ arising from the Bruhat-Tits building for $\\PGL_3(F)$ was studied in \\cite{KL}, where a closed form expression was obtained by a combinatorial argument. This identity can be rephrased using operators on vertices, edges, and directed chambers of $X_\\Gamma$. In this paper we reprove the zeta identity from a different aspect by analyzing the eigenvalues of these operators using representation theory. As a byproduct, we obtain equivalent criteria for a Ramanujan complex in terms of the eigenvalues of the operators on vertices, edges, and di"},"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":"0809.1401","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-09-08T18:36:08Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"d4e8f29a63166347254d68bc97507c7537622e2a3791666707918756a87bc9c8","abstract_canon_sha256":"55bc04661ea16e8e442505a989e2a02f51139c0808cc2fb7affa3e28a43737b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:58.094253Z","signature_b64":"07tZyL6WQ2g7lQWDs7Gjkv/rHf/ez93pxqK0JyMphPmUoLu8RKus9IyallNAPrh/3Np7GKMUJmrtBOHxHtaSBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2134904fbcdd439c673ea2b49cb6e45e4e4fad35fc668b559ec87ec9e23646f0","last_reissued_at":"2026-05-18T03:44:58.093755Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:58.093755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Zeta Functions of Complexes from $\\PGL(3)$: a Representation-theoretic Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Chian-Jen Wang, Ming-Hsuan Kang, Wen-Ching Winnie Li","submitted_at":"2008-09-08T18:36:08Z","abstract_excerpt":"The zeta function attached to a finite complex $X_\\Gamma$ arising from the Bruhat-Tits building for $\\PGL_3(F)$ was studied in \\cite{KL}, where a closed form expression was obtained by a combinatorial argument. This identity can be rephrased using operators on vertices, edges, and directed chambers of $X_\\Gamma$. In this paper we reprove the zeta identity from a different aspect by analyzing the eigenvalues of these operators using representation theory. As a byproduct, we obtain equivalent criteria for a Ramanujan complex in terms of the eigenvalues of the operators on vertices, edges, and di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.1401","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":"0809.1401","created_at":"2026-05-18T03:44:58.093820+00:00"},{"alias_kind":"arxiv_version","alias_value":"0809.1401v3","created_at":"2026-05-18T03:44:58.093820+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.1401","created_at":"2026-05-18T03:44:58.093820+00:00"},{"alias_kind":"pith_short_12","alias_value":"EE2JAT543VBZ","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"EE2JAT543VBZYZZ6","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"EE2JAT54","created_at":"2026-05-18T12:25:57.157939+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/EE2JAT543VBZYZZ6UK2JZNXELZ","json":"https://pith.science/pith/EE2JAT543VBZYZZ6UK2JZNXELZ.json","graph_json":"https://pith.science/api/pith-number/EE2JAT543VBZYZZ6UK2JZNXELZ/graph.json","events_json":"https://pith.science/api/pith-number/EE2JAT543VBZYZZ6UK2JZNXELZ/events.json","paper":"https://pith.science/paper/EE2JAT54"},"agent_actions":{"view_html":"https://pith.science/pith/EE2JAT543VBZYZZ6UK2JZNXELZ","download_json":"https://pith.science/pith/EE2JAT543VBZYZZ6UK2JZNXELZ.json","view_paper":"https://pith.science/paper/EE2JAT54","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0809.1401&json=true","fetch_graph":"https://pith.science/api/pith-number/EE2JAT543VBZYZZ6UK2JZNXELZ/graph.json","fetch_events":"https://pith.science/api/pith-number/EE2JAT543VBZYZZ6UK2JZNXELZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EE2JAT543VBZYZZ6UK2JZNXELZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EE2JAT543VBZYZZ6UK2JZNXELZ/action/storage_attestation","attest_author":"https://pith.science/pith/EE2JAT543VBZYZZ6UK2JZNXELZ/action/author_attestation","sign_citation":"https://pith.science/pith/EE2JAT543VBZYZZ6UK2JZNXELZ/action/citation_signature","submit_replication":"https://pith.science/pith/EE2JAT543VBZYZZ6UK2JZNXELZ/action/replication_record"}},"created_at":"2026-05-18T03:44:58.093820+00:00","updated_at":"2026-05-18T03:44:58.093820+00:00"}