{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ROUIJG3NZBVYKPICFVOBNEVHY5","short_pith_number":"pith:ROUIJG3N","schema_version":"1.0","canonical_sha256":"8ba8849b6dc86b853d022d5c1692a7c75e6a1563237d598b66b5a6456748b375","source":{"kind":"arxiv","id":"1409.1498","version":1},"attestation_state":"computed","paper":{"title":"Complete Monotonicity of classical theta functions and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"A. Raouf Chouikha","submitted_at":"2014-09-04T17:23:52Z","abstract_excerpt":"We produce trigonometric expansions for Jacobi theta functions\\\\ $\\theta_j(u,\\tau), j=1,2,3,4$\\ where $\\tau=i\\pi t, t > 0$. This permits us to prove that\\ $\\log \\frac{\\theta_j(u, t)}{\\theta_j(0, t)}, j=2,3,4$ and $\\log \\frac{\\theta_1(u, t)}{\\pi \\theta'_1(0, t)}$ as well as $\\frac{\\frac{\\delta\\theta_j}{\\delta u}}{\\theta_j}$ as functions of $t$ are completely monotonic. We also interested in the quotients $S_j(u,v,t) = \\frac{\\theta_j(u/2,i\\pi t)}{\\theta_j(u/2,i\\pi t)}$. For fixed $u,v$ such that $0\\leq u < v < 1$ we prove that the functions $\\frac{(\\frac{\\delta}{\\delta t}S_j)}{S_j}$ for $j=1,4$ "},"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":"1409.1498","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-09-04T17:23:52Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"c7746f5c702497e199ee0f09ef6733404f2fc42e889bb5d7e1a16eae01cbb5da","abstract_canon_sha256":"9e07c58af41ec9deeb3dbaae6a45c89cc4b9847ed86e916c7bc66e098c3b3309"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:18.480624Z","signature_b64":"fu0NU8p5xtWPE7HisQ6syyVM+u7xBT6wpCNNA2gOBry4oGSdwxJYLipT0M0PWnX+lmBGrCprY7bgexgRpZauCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ba8849b6dc86b853d022d5c1692a7c75e6a1563237d598b66b5a6456748b375","last_reissued_at":"2026-05-18T02:43:18.480102Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:18.480102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complete Monotonicity of classical theta functions and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"A. Raouf Chouikha","submitted_at":"2014-09-04T17:23:52Z","abstract_excerpt":"We produce trigonometric expansions for Jacobi theta functions\\\\ $\\theta_j(u,\\tau), j=1,2,3,4$\\ where $\\tau=i\\pi t, t > 0$. This permits us to prove that\\ $\\log \\frac{\\theta_j(u, t)}{\\theta_j(0, t)}, j=2,3,4$ and $\\log \\frac{\\theta_1(u, t)}{\\pi \\theta'_1(0, t)}$ as well as $\\frac{\\frac{\\delta\\theta_j}{\\delta u}}{\\theta_j}$ as functions of $t$ are completely monotonic. We also interested in the quotients $S_j(u,v,t) = \\frac{\\theta_j(u/2,i\\pi t)}{\\theta_j(u/2,i\\pi t)}$. For fixed $u,v$ such that $0\\leq u < v < 1$ we prove that the functions $\\frac{(\\frac{\\delta}{\\delta t}S_j)}{S_j}$ for $j=1,4$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1498","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":"1409.1498","created_at":"2026-05-18T02:43:18.480174+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.1498v1","created_at":"2026-05-18T02:43:18.480174+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1498","created_at":"2026-05-18T02:43:18.480174+00:00"},{"alias_kind":"pith_short_12","alias_value":"ROUIJG3NZBVY","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"ROUIJG3NZBVYKPIC","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"ROUIJG3N","created_at":"2026-05-18T12:28:46.137349+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/ROUIJG3NZBVYKPICFVOBNEVHY5","json":"https://pith.science/pith/ROUIJG3NZBVYKPICFVOBNEVHY5.json","graph_json":"https://pith.science/api/pith-number/ROUIJG3NZBVYKPICFVOBNEVHY5/graph.json","events_json":"https://pith.science/api/pith-number/ROUIJG3NZBVYKPICFVOBNEVHY5/events.json","paper":"https://pith.science/paper/ROUIJG3N"},"agent_actions":{"view_html":"https://pith.science/pith/ROUIJG3NZBVYKPICFVOBNEVHY5","download_json":"https://pith.science/pith/ROUIJG3NZBVYKPICFVOBNEVHY5.json","view_paper":"https://pith.science/paper/ROUIJG3N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.1498&json=true","fetch_graph":"https://pith.science/api/pith-number/ROUIJG3NZBVYKPICFVOBNEVHY5/graph.json","fetch_events":"https://pith.science/api/pith-number/ROUIJG3NZBVYKPICFVOBNEVHY5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ROUIJG3NZBVYKPICFVOBNEVHY5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ROUIJG3NZBVYKPICFVOBNEVHY5/action/storage_attestation","attest_author":"https://pith.science/pith/ROUIJG3NZBVYKPICFVOBNEVHY5/action/author_attestation","sign_citation":"https://pith.science/pith/ROUIJG3NZBVYKPICFVOBNEVHY5/action/citation_signature","submit_replication":"https://pith.science/pith/ROUIJG3NZBVYKPICFVOBNEVHY5/action/replication_record"}},"created_at":"2026-05-18T02:43:18.480174+00:00","updated_at":"2026-05-18T02:43:18.480174+00:00"}