{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:V6HZ6WEGQQKFPJJIYJTBJYPL2I","short_pith_number":"pith:V6HZ6WEG","canonical_record":{"source":{"id":"1503.03119","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-10T23:03:20Z","cross_cats_sorted":[],"title_canon_sha256":"5b106cd109177a082189497e208a28dc655ae5da6533dc8cda116013efa49631","abstract_canon_sha256":"3653b6658e782920d8bca41df63c2ae0820ba26ccd1f9df47e886572ca88f80b"},"schema_version":"1.0"},"canonical_sha256":"af8f9f5886841457a528c26614e1ebd2062e7d813a8fc46f8e4194ad73a515f2","source":{"kind":"arxiv","id":"1503.03119","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03119","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03119v2","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03119","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"V6HZ6WEGQQKF","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"V6HZ6WEGQQKFPJJI","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"V6HZ6WEG","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:V6HZ6WEGQQKFPJJIYJTBJYPL2I","target":"record","payload":{"canonical_record":{"source":{"id":"1503.03119","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-10T23:03:20Z","cross_cats_sorted":[],"title_canon_sha256":"5b106cd109177a082189497e208a28dc655ae5da6533dc8cda116013efa49631","abstract_canon_sha256":"3653b6658e782920d8bca41df63c2ae0820ba26ccd1f9df47e886572ca88f80b"},"schema_version":"1.0"},"canonical_sha256":"af8f9f5886841457a528c26614e1ebd2062e7d813a8fc46f8e4194ad73a515f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:13.645980Z","signature_b64":"Jj/Gxa7R8LEY+LNrYiPiOHP5Yf2VPbJ4MMfY5TxMgdyvBPgjo0pOsfnObRxa/P+ItKn57+53LtdUuPj/jm7cDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af8f9f5886841457a528c26614e1ebd2062e7d813a8fc46f8e4194ad73a515f2","last_reissued_at":"2026-05-18T00:42:13.645215Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:13.645215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.03119","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YTlYcbFuF7pZwmT+Zn8frzs1RyEovFMwgbnBj6uXEWw7saanxfksN0Qc2kWQVttTf3elaBFTVrsYUCn4NQXbDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:03:29.852642Z"},"content_sha256":"102a79807a1540e0d099398e034eb45590c6c2d90aeb839cf6ca151aeac4e62c","schema_version":"1.0","event_id":"sha256:102a79807a1540e0d099398e034eb45590c6c2d90aeb839cf6ca151aeac4e62c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:V6HZ6WEGQQKFPJJIYJTBJYPL2I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distribution of the values of the derivative of the Dirichlet $L$-functions at its $a$-points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kamel Mazhouda, Mohamed Ta\\\"ib Jakhlouti","submitted_at":"2015-03-10T23:03:20Z","abstract_excerpt":"In this paper, we study the value distribution of the derivative of a Dirichlet $L$-function $L'(s,\\chi)$ at the $a$-points $\\rho_{a,\\chi}=\\beta_{a,\\chi}+i\\gamma_{a,\\chi}$ of $L(s,\\chi).$ We give an asymptotic formula for the sum $$\\sum_{\\rho_{a,\\chi};\\ 0<\\gamma_{a,\\chi}\\leq T}L'\\left(\\rho_{a,\\chi},\\chi\\right) X^{\\rho_{a,\\chi}}\\ \\ \\hbox{as}\\ \\\n  T\\longrightarrow \\infty,$$ where $X$ is a fixed positive number and $\\chi$ is a primitive character $\\mod q$. This work continues the investigations of Fujii \\cite{2,3,4}, Garunk$\\check{s}$tis \\& Steuding \\cite{7} and the authors \\cite{12}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03119","kind":"arxiv","version":2},"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":"2026-05-18T00:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0LPlIc+bgLLTY7gKzcpHLyFR89gbr1kHkP+YAYU7jFFgDLcde3/ZUXegetFJijUMNOzicJrLOKdvBTGKxB/gCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:03:29.852986Z"},"content_sha256":"b4a45011e3ee5bf994ee151ec097ea6d3246e74785ba17c3dd04ad3c337d8c19","schema_version":"1.0","event_id":"sha256:b4a45011e3ee5bf994ee151ec097ea6d3246e74785ba17c3dd04ad3c337d8c19"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V6HZ6WEGQQKFPJJIYJTBJYPL2I/bundle.json","state_url":"https://pith.science/pith/V6HZ6WEGQQKFPJJIYJTBJYPL2I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V6HZ6WEGQQKFPJJIYJTBJYPL2I/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":"2026-06-26T14:03:29Z","links":{"resolver":"https://pith.science/pith/V6HZ6WEGQQKFPJJIYJTBJYPL2I","bundle":"https://pith.science/pith/V6HZ6WEGQQKFPJJIYJTBJYPL2I/bundle.json","state":"https://pith.science/pith/V6HZ6WEGQQKFPJJIYJTBJYPL2I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V6HZ6WEGQQKFPJJIYJTBJYPL2I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:V6HZ6WEGQQKFPJJIYJTBJYPL2I","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":"3653b6658e782920d8bca41df63c2ae0820ba26ccd1f9df47e886572ca88f80b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-10T23:03:20Z","title_canon_sha256":"5b106cd109177a082189497e208a28dc655ae5da6533dc8cda116013efa49631"},"schema_version":"1.0","source":{"id":"1503.03119","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03119","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03119v2","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03119","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"V6HZ6WEGQQKF","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"V6HZ6WEGQQKFPJJI","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"V6HZ6WEG","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:b4a45011e3ee5bf994ee151ec097ea6d3246e74785ba17c3dd04ad3c337d8c19","target":"graph","created_at":"2026-05-18T00:42:13Z","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":"In this paper, we study the value distribution of the derivative of a Dirichlet $L$-function $L'(s,\\chi)$ at the $a$-points $\\rho_{a,\\chi}=\\beta_{a,\\chi}+i\\gamma_{a,\\chi}$ of $L(s,\\chi).$ We give an asymptotic formula for the sum $$\\sum_{\\rho_{a,\\chi};\\ 0<\\gamma_{a,\\chi}\\leq T}L'\\left(\\rho_{a,\\chi},\\chi\\right) X^{\\rho_{a,\\chi}}\\ \\ \\hbox{as}\\ \\\n  T\\longrightarrow \\infty,$$ where $X$ is a fixed positive number and $\\chi$ is a primitive character $\\mod q$. This work continues the investigations of Fujii \\cite{2,3,4}, Garunk$\\check{s}$tis \\& Steuding \\cite{7} and the authors \\cite{12}.","authors_text":"Kamel Mazhouda, Mohamed Ta\\\"ib Jakhlouti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-10T23:03:20Z","title":"Distribution of the values of the derivative of the Dirichlet $L$-functions at its $a$-points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03119","kind":"arxiv","version":2},"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":"sha256:102a79807a1540e0d099398e034eb45590c6c2d90aeb839cf6ca151aeac4e62c","target":"record","created_at":"2026-05-18T00:42:13Z","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":"3653b6658e782920d8bca41df63c2ae0820ba26ccd1f9df47e886572ca88f80b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-10T23:03:20Z","title_canon_sha256":"5b106cd109177a082189497e208a28dc655ae5da6533dc8cda116013efa49631"},"schema_version":"1.0","source":{"id":"1503.03119","kind":"arxiv","version":2}},"canonical_sha256":"af8f9f5886841457a528c26614e1ebd2062e7d813a8fc46f8e4194ad73a515f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af8f9f5886841457a528c26614e1ebd2062e7d813a8fc46f8e4194ad73a515f2","first_computed_at":"2026-05-18T00:42:13.645215Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:13.645215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jj/Gxa7R8LEY+LNrYiPiOHP5Yf2VPbJ4MMfY5TxMgdyvBPgjo0pOsfnObRxa/P+ItKn57+53LtdUuPj/jm7cDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:13.645980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.03119","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:102a79807a1540e0d099398e034eb45590c6c2d90aeb839cf6ca151aeac4e62c","sha256:b4a45011e3ee5bf994ee151ec097ea6d3246e74785ba17c3dd04ad3c337d8c19"],"state_sha256":"4fa72854c7e2528b36a626eb528a056237bc064797181f57f57a008d84396be5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ocIi4dSByF0ZgB/Tg3TLBd00S7oRRHf/v3sknZ95XOeGx8RGbReu5v0JF8v6eNdB4j4XXsHxZwduN4q9gea1AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T14:03:29.854897Z","bundle_sha256":"4bca063e0b330605c8db1d0509228f32603e6a583ab1cdada04c3702601ffbb0"}}