{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:CQHW263B2OZGIVKBWTXUEBYMUO","short_pith_number":"pith:CQHW263B","schema_version":"1.0","canonical_sha256":"140f6d7b61d3b2645541b4ef42070ca39cae54070620e5d3fe7374cc5a87c9fa","source":{"kind":"arxiv","id":"1809.06921","version":1},"attestation_state":"computed","paper":{"title":"Special values of derivatives of $L$-series and generalized Stieltjes constants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"M. Ram Murty, Siddhi Pathak","submitted_at":"2018-09-18T20:27:55Z","abstract_excerpt":"The connection between derivatives of $L(s,f)$ for periodic arithmetical functions $f$ at $s=1$ and generalized Stieltjes constants has been noted earlier. In this paper, we utilize this link to throw light on the arithmetic nature of $L'(1,f)$ and certain Stieltjes constants. In particular, if $p$ is an odd prime greater than $7$, then we deduce the transcendence of at least $(p-7)/2$ of the generalized Stieltjes constants, $\\{ \\gamma_1(a,p) : 1 \\leq a < p \\}$, conditional on a conjecture of S. Gun, M. R. Murty and P. Rath."},"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":"1809.06921","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-18T20:27:55Z","cross_cats_sorted":[],"title_canon_sha256":"c4734186856397695ff6ed3058d63c192f7aca65994b7b817e13c6c648e1dcde","abstract_canon_sha256":"add36f7a6e7517a25a83893f06a8b145a4ee5ae6248748f854d934da03f91dd6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:21.152728Z","signature_b64":"U2Rl19dRfoOyGCBslhj4NB1bSHYYziMl8QQjzkmKNbvtKy0HUri3HSz3i5A6MAVhT2/GOmBODbzDg0JUpPFfAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"140f6d7b61d3b2645541b4ef42070ca39cae54070620e5d3fe7374cc5a87c9fa","last_reissued_at":"2026-05-18T00:05:21.152200Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:21.152200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Special values of derivatives of $L$-series and generalized Stieltjes constants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"M. Ram Murty, Siddhi Pathak","submitted_at":"2018-09-18T20:27:55Z","abstract_excerpt":"The connection between derivatives of $L(s,f)$ for periodic arithmetical functions $f$ at $s=1$ and generalized Stieltjes constants has been noted earlier. In this paper, we utilize this link to throw light on the arithmetic nature of $L'(1,f)$ and certain Stieltjes constants. In particular, if $p$ is an odd prime greater than $7$, then we deduce the transcendence of at least $(p-7)/2$ of the generalized Stieltjes constants, $\\{ \\gamma_1(a,p) : 1 \\leq a < p \\}$, conditional on a conjecture of S. Gun, M. R. Murty and P. Rath."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06921","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":"1809.06921","created_at":"2026-05-18T00:05:21.152282+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.06921v1","created_at":"2026-05-18T00:05:21.152282+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06921","created_at":"2026-05-18T00:05:21.152282+00:00"},{"alias_kind":"pith_short_12","alias_value":"CQHW263B2OZG","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"CQHW263B2OZGIVKB","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"CQHW263B","created_at":"2026-05-18T12:32:16.446611+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/CQHW263B2OZGIVKBWTXUEBYMUO","json":"https://pith.science/pith/CQHW263B2OZGIVKBWTXUEBYMUO.json","graph_json":"https://pith.science/api/pith-number/CQHW263B2OZGIVKBWTXUEBYMUO/graph.json","events_json":"https://pith.science/api/pith-number/CQHW263B2OZGIVKBWTXUEBYMUO/events.json","paper":"https://pith.science/paper/CQHW263B"},"agent_actions":{"view_html":"https://pith.science/pith/CQHW263B2OZGIVKBWTXUEBYMUO","download_json":"https://pith.science/pith/CQHW263B2OZGIVKBWTXUEBYMUO.json","view_paper":"https://pith.science/paper/CQHW263B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.06921&json=true","fetch_graph":"https://pith.science/api/pith-number/CQHW263B2OZGIVKBWTXUEBYMUO/graph.json","fetch_events":"https://pith.science/api/pith-number/CQHW263B2OZGIVKBWTXUEBYMUO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CQHW263B2OZGIVKBWTXUEBYMUO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CQHW263B2OZGIVKBWTXUEBYMUO/action/storage_attestation","attest_author":"https://pith.science/pith/CQHW263B2OZGIVKBWTXUEBYMUO/action/author_attestation","sign_citation":"https://pith.science/pith/CQHW263B2OZGIVKBWTXUEBYMUO/action/citation_signature","submit_replication":"https://pith.science/pith/CQHW263B2OZGIVKBWTXUEBYMUO/action/replication_record"}},"created_at":"2026-05-18T00:05:21.152282+00:00","updated_at":"2026-05-18T00:05:21.152282+00:00"}