{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:T7NEXMI7Z4JFGEWNSM3PKKEKMN","short_pith_number":"pith:T7NEXMI7","schema_version":"1.0","canonical_sha256":"9fda4bb11fcf125312cd9336f5288a6343eb8e8b614cb3c1e6ef5dad2570fff7","source":{"kind":"arxiv","id":"2509.06390","version":1},"attestation_state":"computed","paper":{"title":"Moments of Higher derivatives of the logarithmic derivative of Dirichlet $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Samprit Ghosh","submitted_at":"2025-09-08T07:21:02Z","abstract_excerpt":"Let $\\chi$ be a non-principal Dirichlet character and $L(s, \\chi)$ be the associated Dirichlet $L$-function. Let us use $\\mathcal{L}(s,\\chi)$ to denote its logarithmic derivative $L'(s, \\chi)/L(s, \\chi)$. We first prove some arithmetic formulas for higher derivatives $\\mathcal{L}^{(r)}(1,\\chi)$. We then investigate their moments. We study the average of $P^{(a,b)}(\\mathcal{L}^{(r)}(1,\\chi))$ as $\\chi$ runs over all non-principal Dirichlet characters with a given large prime conductor $m$, where $P^{(a,b)}(z) = z^a \\overline{z}^b$."},"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":"2509.06390","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-09-08T07:21:02Z","cross_cats_sorted":[],"title_canon_sha256":"bff0b342b4b3e4c0d774bb6c4c13ab700ac4659c932ab43f94081ea6bd3906f1","abstract_canon_sha256":"b4764dc9597c7def56d3915aa0ba010e29a475655fe169a33ff000980fb649b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:06:34.903305Z","signature_b64":"m70CnqdCQJGIZ/p4eNwMqG5VjTynBlrMSZY+wJyI99kxjqvLC5ZhuDi6OMIP3fx9Yrq+JmSjk9DviXqNni+YDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fda4bb11fcf125312cd9336f5288a6343eb8e8b614cb3c1e6ef5dad2570fff7","last_reissued_at":"2026-07-05T12:06:34.902905Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:06:34.902905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Moments of Higher derivatives of the logarithmic derivative of Dirichlet $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Samprit Ghosh","submitted_at":"2025-09-08T07:21:02Z","abstract_excerpt":"Let $\\chi$ be a non-principal Dirichlet character and $L(s, \\chi)$ be the associated Dirichlet $L$-function. Let us use $\\mathcal{L}(s,\\chi)$ to denote its logarithmic derivative $L'(s, \\chi)/L(s, \\chi)$. We first prove some arithmetic formulas for higher derivatives $\\mathcal{L}^{(r)}(1,\\chi)$. We then investigate their moments. We study the average of $P^{(a,b)}(\\mathcal{L}^{(r)}(1,\\chi))$ as $\\chi$ runs over all non-principal Dirichlet characters with a given large prime conductor $m$, where $P^{(a,b)}(z) = z^a \\overline{z}^b$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.06390","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.06390/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2509.06390","created_at":"2026-07-05T12:06:34.902959+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.06390v1","created_at":"2026-07-05T12:06:34.902959+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.06390","created_at":"2026-07-05T12:06:34.902959+00:00"},{"alias_kind":"pith_short_12","alias_value":"T7NEXMI7Z4JF","created_at":"2026-07-05T12:06:34.902959+00:00"},{"alias_kind":"pith_short_16","alias_value":"T7NEXMI7Z4JFGEWN","created_at":"2026-07-05T12:06:34.902959+00:00"},{"alias_kind":"pith_short_8","alias_value":"T7NEXMI7","created_at":"2026-07-05T12:06:34.902959+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/T7NEXMI7Z4JFGEWNSM3PKKEKMN","json":"https://pith.science/pith/T7NEXMI7Z4JFGEWNSM3PKKEKMN.json","graph_json":"https://pith.science/api/pith-number/T7NEXMI7Z4JFGEWNSM3PKKEKMN/graph.json","events_json":"https://pith.science/api/pith-number/T7NEXMI7Z4JFGEWNSM3PKKEKMN/events.json","paper":"https://pith.science/paper/T7NEXMI7"},"agent_actions":{"view_html":"https://pith.science/pith/T7NEXMI7Z4JFGEWNSM3PKKEKMN","download_json":"https://pith.science/pith/T7NEXMI7Z4JFGEWNSM3PKKEKMN.json","view_paper":"https://pith.science/paper/T7NEXMI7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.06390&json=true","fetch_graph":"https://pith.science/api/pith-number/T7NEXMI7Z4JFGEWNSM3PKKEKMN/graph.json","fetch_events":"https://pith.science/api/pith-number/T7NEXMI7Z4JFGEWNSM3PKKEKMN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T7NEXMI7Z4JFGEWNSM3PKKEKMN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T7NEXMI7Z4JFGEWNSM3PKKEKMN/action/storage_attestation","attest_author":"https://pith.science/pith/T7NEXMI7Z4JFGEWNSM3PKKEKMN/action/author_attestation","sign_citation":"https://pith.science/pith/T7NEXMI7Z4JFGEWNSM3PKKEKMN/action/citation_signature","submit_replication":"https://pith.science/pith/T7NEXMI7Z4JFGEWNSM3PKKEKMN/action/replication_record"}},"created_at":"2026-07-05T12:06:34.902959+00:00","updated_at":"2026-07-05T12:06:34.902959+00:00"}