{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ARNLFLO7AGHU2ZFDYBAABEWV3H","short_pith_number":"pith:ARNLFLO7","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"},"canonical_sha256":"045ab2addf018f4d64a3c0400092d5d9c1e42d04629d1e55047319bc03f6e245","source":{"kind":"arxiv","id":"1902.03846","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03846","created_at":"2026-05-17T23:54:17Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03846v1","created_at":"2026-05-17T23:54:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03846","created_at":"2026-05-17T23:54:17Z"},{"alias_kind":"pith_short_12","alias_value":"ARNLFLO7AGHU","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"ARNLFLO7AGHU2ZFD","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"ARNLFLO7","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ARNLFLO7AGHU2ZFDYBAABEWV3H","target":"record","payload":{"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"},"canonical_sha256":"045ab2addf018f4d64a3c0400092d5d9c1e42d04629d1e55047319bc03f6e245","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"},"source_kind":"arxiv","source_id":"1902.03846","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:54:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jr/yFFoDk1itbh970uiDPqEj9W2vOIRDWk5PuSZFVH89mfyAHSyGn1qbfjM4C1rrb+pyKMOANB0F7RsRWS0WBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:45:40.348877Z"},"content_sha256":"cf037513e3ab3bb7f5d61a680fd53838147d391fbfc81e76b678b913b946d499","schema_version":"1.0","event_id":"sha256:cf037513e3ab3bb7f5d61a680fd53838147d391fbfc81e76b678b913b946d499"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ARNLFLO7AGHU2ZFDYBAABEWV3H","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:54:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lr6gSzhCGRWN/EOljrgHA2LovWsBvCasfvbClYdPLOUyNzVMFikU7oN7hDeMjpjCZ4F5qWvrXCxzS0D7oxZoCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:45:40.349204Z"},"content_sha256":"68edc7ec71392dd979fcd202b08c087acf260539605ea6d858529a0f75ed1359","schema_version":"1.0","event_id":"sha256:68edc7ec71392dd979fcd202b08c087acf260539605ea6d858529a0f75ed1359"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ARNLFLO7AGHU2ZFDYBAABEWV3H/bundle.json","state_url":"https://pith.science/pith/ARNLFLO7AGHU2ZFDYBAABEWV3H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ARNLFLO7AGHU2ZFDYBAABEWV3H/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T22:45:40Z","links":{"resolver":"https://pith.science/pith/ARNLFLO7AGHU2ZFDYBAABEWV3H","bundle":"https://pith.science/pith/ARNLFLO7AGHU2ZFDYBAABEWV3H/bundle.json","state":"https://pith.science/pith/ARNLFLO7AGHU2ZFDYBAABEWV3H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ARNLFLO7AGHU2ZFDYBAABEWV3H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ARNLFLO7AGHU2ZFDYBAABEWV3H","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c887878a77c7df071ae4c2a3914a278f1d9606c6774aff9ebdc0a7b0253973c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-02-11T12:50:15Z","title_canon_sha256":"962770e12997cefbfd277c9ee167ef2a651c86cb2e880decad14e3b194baca0d"},"schema_version":"1.0","source":{"id":"1902.03846","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03846","created_at":"2026-05-17T23:54:17Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03846v1","created_at":"2026-05-17T23:54:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03846","created_at":"2026-05-17T23:54:17Z"},{"alias_kind":"pith_short_12","alias_value":"ARNLFLO7AGHU","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"ARNLFLO7AGHU2ZFD","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"ARNLFLO7","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:68edc7ec71392dd979fcd202b08c087acf260539605ea6d858529a0f75ed1359","target":"graph","created_at":"2026-05-17T23:54:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Rong Ma, Yana Niu, Yulong Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-02-11T12:50:15Z","title":"On asymptotic properties of the generalized Dirichlet $L$-functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03846","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cf037513e3ab3bb7f5d61a680fd53838147d391fbfc81e76b678b913b946d499","target":"record","created_at":"2026-05-17T23:54:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c887878a77c7df071ae4c2a3914a278f1d9606c6774aff9ebdc0a7b0253973c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-02-11T12:50:15Z","title_canon_sha256":"962770e12997cefbfd277c9ee167ef2a651c86cb2e880decad14e3b194baca0d"},"schema_version":"1.0","source":{"id":"1902.03846","kind":"arxiv","version":1}},"canonical_sha256":"045ab2addf018f4d64a3c0400092d5d9c1e42d04629d1e55047319bc03f6e245","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"045ab2addf018f4d64a3c0400092d5d9c1e42d04629d1e55047319bc03f6e245","first_computed_at":"2026-05-17T23:54:17.713431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:17.713431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qMSCXxH9fhhJ8rqI+8RMCXiCdNEXD+6OF7BeBne3C4mAr77N1xdPykpNjcZIDpbdIAFOCzO5npuwCjal8a4oCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:17.713989Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.03846","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf037513e3ab3bb7f5d61a680fd53838147d391fbfc81e76b678b913b946d499","sha256:68edc7ec71392dd979fcd202b08c087acf260539605ea6d858529a0f75ed1359"],"state_sha256":"a21fe1d7cad22754954b2e65542bac3c7f16f18b8724f797dfaa501388270fd4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gzpohxt4WGK/iTINfhXi0o6GVz/kPwX1CEywecJgmo8zrL4Fq0U+YAImNKL0z5VDQ+FNANCRXqsmTAQ/Kg6uBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T22:45:40.351250Z","bundle_sha256":"635afadd4255394403d67c75b1a038b4560096bb7040f47266e085d3ccd07a9f"}}