{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:DH25ERNC6NPL54DF57Y5XGV52Z","short_pith_number":"pith:DH25ERNC","schema_version":"1.0","canonical_sha256":"19f5d245a2f35ebef065eff1db9abdd67a27d0e1b9062962f9ce5927b977b4a3","source":{"kind":"arxiv","id":"math/0702209","version":2},"attestation_state":"computed","paper":{"title":"Ruelle type L-functions versus determinants of Laplacians for torsion free abelian groups","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Masato Wakayama, Nobushige Kurokawa, Yoshinori Yamasaki","submitted_at":"2007-02-08T02:46:30Z","abstract_excerpt":"We study Ruelle's type zeta and $L$-functions for a torsion free abelian group $\\G$ of rank $\\n\\ge 2$ defined via an Euler product. It is shown that the imaginary axis is a natural boundary of this zeta function when $\\n=2,4$ and 8, and in particular, such a zeta function has no determinant expression. Thus, conversely, expressions like Euler's product for the determinant of the Laplacians of the torus $\\bR^{\\n}/\\G$ defined via zeta regularizations are investigated. Also, the limit behavior of an arithmetic function arising from the Ruelle type zeta function is observed."},"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/0702209","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2007-02-08T02:46:30Z","cross_cats_sorted":[],"title_canon_sha256":"11c4994c9bd2f76604b96ba340670f83901c02b07a0eb1b450787a5d661dc3f9","abstract_canon_sha256":"9da03a03fc2e7c506df8504f802670dbbdffd3c49109b7f53d3b3d4c0954a42e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:03.897962Z","signature_b64":"KUpeVPnhk7JRbSs1ZIBMD0M/XRX8iCbBgUbgA/iWg5NZ/6BE0YyjeRP77agtde36/fHBbBqmiSyIMvfpIWpIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19f5d245a2f35ebef065eff1db9abdd67a27d0e1b9062962f9ce5927b977b4a3","last_reissued_at":"2026-05-18T03:39:03.897525Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:03.897525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ruelle type L-functions versus determinants of Laplacians for torsion free abelian groups","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Masato Wakayama, Nobushige Kurokawa, Yoshinori Yamasaki","submitted_at":"2007-02-08T02:46:30Z","abstract_excerpt":"We study Ruelle's type zeta and $L$-functions for a torsion free abelian group $\\G$ of rank $\\n\\ge 2$ defined via an Euler product. It is shown that the imaginary axis is a natural boundary of this zeta function when $\\n=2,4$ and 8, and in particular, such a zeta function has no determinant expression. Thus, conversely, expressions like Euler's product for the determinant of the Laplacians of the torus $\\bR^{\\n}/\\G$ defined via zeta regularizations are investigated. Also, the limit behavior of an arithmetic function arising from the Ruelle type zeta function is observed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702209","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":"math/0702209","created_at":"2026-05-18T03:39:03.897587+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0702209v2","created_at":"2026-05-18T03:39:03.897587+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702209","created_at":"2026-05-18T03:39:03.897587+00:00"},{"alias_kind":"pith_short_12","alias_value":"DH25ERNC6NPL","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"DH25ERNC6NPL54DF","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"DH25ERNC","created_at":"2026-05-18T12:25:55.427421+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/DH25ERNC6NPL54DF57Y5XGV52Z","json":"https://pith.science/pith/DH25ERNC6NPL54DF57Y5XGV52Z.json","graph_json":"https://pith.science/api/pith-number/DH25ERNC6NPL54DF57Y5XGV52Z/graph.json","events_json":"https://pith.science/api/pith-number/DH25ERNC6NPL54DF57Y5XGV52Z/events.json","paper":"https://pith.science/paper/DH25ERNC"},"agent_actions":{"view_html":"https://pith.science/pith/DH25ERNC6NPL54DF57Y5XGV52Z","download_json":"https://pith.science/pith/DH25ERNC6NPL54DF57Y5XGV52Z.json","view_paper":"https://pith.science/paper/DH25ERNC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0702209&json=true","fetch_graph":"https://pith.science/api/pith-number/DH25ERNC6NPL54DF57Y5XGV52Z/graph.json","fetch_events":"https://pith.science/api/pith-number/DH25ERNC6NPL54DF57Y5XGV52Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DH25ERNC6NPL54DF57Y5XGV52Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DH25ERNC6NPL54DF57Y5XGV52Z/action/storage_attestation","attest_author":"https://pith.science/pith/DH25ERNC6NPL54DF57Y5XGV52Z/action/author_attestation","sign_citation":"https://pith.science/pith/DH25ERNC6NPL54DF57Y5XGV52Z/action/citation_signature","submit_replication":"https://pith.science/pith/DH25ERNC6NPL54DF57Y5XGV52Z/action/replication_record"}},"created_at":"2026-05-18T03:39:03.897587+00:00","updated_at":"2026-05-18T03:39:03.897587+00:00"}