{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:GPKOQGK5RM7KZONTNJMWURHZPO","short_pith_number":"pith:GPKOQGK5","schema_version":"1.0","canonical_sha256":"33d4e8195d8b3eacb9b36a596a44f97b9d1975d8de13edda7a10282993f4df1b","source":{"kind":"arxiv","id":"1101.4786","version":2},"attestation_state":"computed","paper":{"title":"The Riemann zeta in terms of the dilogarithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Claudio Cacciapuoti, Sergio Albeverio","submitted_at":"2011-01-25T12:19:06Z","abstract_excerpt":"We give a representation of the classical Riemann $\\zeta$-function in the half plane $\\Re s>0$ in terms of a Mellin transform involving the real part of the dilogarithm function with an argument on the unit circle (associated Clausen $Gl_2$-function). We also derive corresponding representations involving the derivatives of the $Gl_2$-function. A generalized symmetrized M\\\"untz-type formula is also derived. For a special choice of test functions it connects to our integral representation of the $\\zeta$-function, providing also a computation of a concrete Mellin transform. Certain formulae invo"},"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":"1101.4786","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-01-25T12:19:06Z","cross_cats_sorted":[],"title_canon_sha256":"fa317d6891d8b9452e28349f1c7ca27cf46dbc245955d93c637f5e33cd751fd7","abstract_canon_sha256":"f3c6f1ea913745cbbf944ed0580ae3144d40eb3805d8d4d8cdd312180086d57e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:59.274999Z","signature_b64":"Z11+VXVJOF8s2c+4KLfb0KKVSNQLeegkI4jmSAYGMXd2Gp8tQ7WQkgQ0liIMLEzawwY3tWcvMSRaDKYc5CCtAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33d4e8195d8b3eacb9b36a596a44f97b9d1975d8de13edda7a10282993f4df1b","last_reissued_at":"2026-05-18T03:48:59.274252Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:59.274252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Riemann zeta in terms of the dilogarithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Claudio Cacciapuoti, Sergio Albeverio","submitted_at":"2011-01-25T12:19:06Z","abstract_excerpt":"We give a representation of the classical Riemann $\\zeta$-function in the half plane $\\Re s>0$ in terms of a Mellin transform involving the real part of the dilogarithm function with an argument on the unit circle (associated Clausen $Gl_2$-function). We also derive corresponding representations involving the derivatives of the $Gl_2$-function. A generalized symmetrized M\\\"untz-type formula is also derived. For a special choice of test functions it connects to our integral representation of the $\\zeta$-function, providing also a computation of a concrete Mellin transform. Certain formulae invo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4786","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":"1101.4786","created_at":"2026-05-18T03:48:59.274380+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.4786v2","created_at":"2026-05-18T03:48:59.274380+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4786","created_at":"2026-05-18T03:48:59.274380+00:00"},{"alias_kind":"pith_short_12","alias_value":"GPKOQGK5RM7K","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"GPKOQGK5RM7KZONT","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"GPKOQGK5","created_at":"2026-05-18T12:26:30.835961+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/GPKOQGK5RM7KZONTNJMWURHZPO","json":"https://pith.science/pith/GPKOQGK5RM7KZONTNJMWURHZPO.json","graph_json":"https://pith.science/api/pith-number/GPKOQGK5RM7KZONTNJMWURHZPO/graph.json","events_json":"https://pith.science/api/pith-number/GPKOQGK5RM7KZONTNJMWURHZPO/events.json","paper":"https://pith.science/paper/GPKOQGK5"},"agent_actions":{"view_html":"https://pith.science/pith/GPKOQGK5RM7KZONTNJMWURHZPO","download_json":"https://pith.science/pith/GPKOQGK5RM7KZONTNJMWURHZPO.json","view_paper":"https://pith.science/paper/GPKOQGK5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.4786&json=true","fetch_graph":"https://pith.science/api/pith-number/GPKOQGK5RM7KZONTNJMWURHZPO/graph.json","fetch_events":"https://pith.science/api/pith-number/GPKOQGK5RM7KZONTNJMWURHZPO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GPKOQGK5RM7KZONTNJMWURHZPO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GPKOQGK5RM7KZONTNJMWURHZPO/action/storage_attestation","attest_author":"https://pith.science/pith/GPKOQGK5RM7KZONTNJMWURHZPO/action/author_attestation","sign_citation":"https://pith.science/pith/GPKOQGK5RM7KZONTNJMWURHZPO/action/citation_signature","submit_replication":"https://pith.science/pith/GPKOQGK5RM7KZONTNJMWURHZPO/action/replication_record"}},"created_at":"2026-05-18T03:48:59.274380+00:00","updated_at":"2026-05-18T03:48:59.274380+00:00"}