{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:ARNLFLO7AGHU2ZFDYBAABEWV3H","short_pith_number":"pith:ARNLFLO7","schema_version":"1.0","canonical_sha256":"045ab2addf018f4d64a3c0400092d5d9c1e42d04629d1e55047319bc03f6e245","source":{"kind":"arxiv","id":"1902.03846","version":1},"attestation_state":"computed","paper":{"title":"On asymptotic properties of the generalized Dirichlet $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Rong Ma, Yana Niu, Yulong Zhang","submitted_at":"2019-02-11T12:50:15Z","abstract_excerpt":"Let $q\\ge3$ be an integer, $\\chi$ denote a Dirichlet character modulo $q$, for any real number $a\\ge 0$, we define the generalized Dirichlet $L$-functions $$ L(s,\\chi,a)=\\sum_{n=1}^{\\infty}\\frac{\\chi(n)}{(n+a)^s}, $$ where $s=\\sigma+it$ with $\\sigma>1$ and $t$ both real. It can be extended to all $s$ by analytic continuation. In this paper, we study the mean value properties of the generalized Dirichlet $L$-functions, and obtain several sharp asymptotic formulae by using analytic method."},"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":"1902.03846","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-02-11T12:50:15Z","cross_cats_sorted":[],"title_canon_sha256":"962770e12997cefbfd277c9ee167ef2a651c86cb2e880decad14e3b194baca0d","abstract_canon_sha256":"c887878a77c7df071ae4c2a3914a278f1d9606c6774aff9ebdc0a7b0253973c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:17.713989Z","signature_b64":"qMSCXxH9fhhJ8rqI+8RMCXiCdNEXD+6OF7BeBne3C4mAr77N1xdPykpNjcZIDpbdIAFOCzO5npuwCjal8a4oCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"045ab2addf018f4d64a3c0400092d5d9c1e42d04629d1e55047319bc03f6e245","last_reissued_at":"2026-05-17T23:54:17.713431Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:17.713431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On asymptotic properties of the generalized Dirichlet $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Rong Ma, Yana Niu, Yulong Zhang","submitted_at":"2019-02-11T12:50:15Z","abstract_excerpt":"Let $q\\ge3$ be an integer, $\\chi$ denote a Dirichlet character modulo $q$, for any real number $a\\ge 0$, we define the generalized Dirichlet $L$-functions $$ L(s,\\chi,a)=\\sum_{n=1}^{\\infty}\\frac{\\chi(n)}{(n+a)^s}, $$ where $s=\\sigma+it$ with $\\sigma>1$ and $t$ both real. It can be extended to all $s$ by analytic continuation. In this paper, we study the mean value properties of the generalized Dirichlet $L$-functions, and obtain several sharp asymptotic formulae by using analytic method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03846","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":"1902.03846","created_at":"2026-05-17T23:54:17.713514+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.03846v1","created_at":"2026-05-17T23:54:17.713514+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03846","created_at":"2026-05-17T23:54:17.713514+00:00"},{"alias_kind":"pith_short_12","alias_value":"ARNLFLO7AGHU","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"ARNLFLO7AGHU2ZFD","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"ARNLFLO7","created_at":"2026-05-18T12:33:12.712433+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/ARNLFLO7AGHU2ZFDYBAABEWV3H","json":"https://pith.science/pith/ARNLFLO7AGHU2ZFDYBAABEWV3H.json","graph_json":"https://pith.science/api/pith-number/ARNLFLO7AGHU2ZFDYBAABEWV3H/graph.json","events_json":"https://pith.science/api/pith-number/ARNLFLO7AGHU2ZFDYBAABEWV3H/events.json","paper":"https://pith.science/paper/ARNLFLO7"},"agent_actions":{"view_html":"https://pith.science/pith/ARNLFLO7AGHU2ZFDYBAABEWV3H","download_json":"https://pith.science/pith/ARNLFLO7AGHU2ZFDYBAABEWV3H.json","view_paper":"https://pith.science/paper/ARNLFLO7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.03846&json=true","fetch_graph":"https://pith.science/api/pith-number/ARNLFLO7AGHU2ZFDYBAABEWV3H/graph.json","fetch_events":"https://pith.science/api/pith-number/ARNLFLO7AGHU2ZFDYBAABEWV3H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ARNLFLO7AGHU2ZFDYBAABEWV3H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ARNLFLO7AGHU2ZFDYBAABEWV3H/action/storage_attestation","attest_author":"https://pith.science/pith/ARNLFLO7AGHU2ZFDYBAABEWV3H/action/author_attestation","sign_citation":"https://pith.science/pith/ARNLFLO7AGHU2ZFDYBAABEWV3H/action/citation_signature","submit_replication":"https://pith.science/pith/ARNLFLO7AGHU2ZFDYBAABEWV3H/action/replication_record"}},"created_at":"2026-05-17T23:54:17.713514+00:00","updated_at":"2026-05-17T23:54:17.713514+00:00"}