{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YXARNIH4PQKEZBTT72YSKKG6JP","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":"09b4a32ea9e8f88bef5b5ffc75f9329ec838c984519a21ec14bb980a1ce9c225","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2012-06-23T19:24:41Z","title_canon_sha256":"ef2e4ff48505da881e8aabf1cc830811de4631b854fcf118aa081cdf7f13a2f0"},"schema_version":"1.0","source":{"id":"1206.5433","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5433","created_at":"2026-05-18T00:10:19Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5433v1","created_at":"2026-05-18T00:10:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5433","created_at":"2026-05-18T00:10:19Z"},{"alias_kind":"pith_short_12","alias_value":"YXARNIH4PQKE","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YXARNIH4PQKEZBTT","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YXARNIH4","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:cc7fd2480e029a91aac68273dfe91c72eebfc3b9936638a9ea97b04a0edca220","target":"graph","created_at":"2026-05-18T00:10:19Z","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 the present paper, we investigate special generalized q-Euler numbers and polynomials. Some earlier results of T. Kim in terms of q-Euler polynomials with weight alpha can be deduced. For presentation of our formulas we apply the method of generating function and p-adic q-integral representation on Zp. We summarize our results as follows. In section 2, by using combinatorial techniques we present two formulas for q-Euler numbers with weight alpha. In section 3, we derive distribution formula (Multiplication Theorem) for Dirichlet type of q-Euler numbers and polynomials with weight . Moreove","authors_text":"Hassan Jolany, Mehmet Acikgoz, Serkan Araci","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2012-06-23T19:24:41Z","title":"On the families of q-Euler numbers and polynomials and their applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5433","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":"sha256:01ac83bd3c8e71c19015efb8a9a2c42e4d95115bc96ae44ee9f9c3ee8743bf36","target":"record","created_at":"2026-05-18T00:10:19Z","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":"09b4a32ea9e8f88bef5b5ffc75f9329ec838c984519a21ec14bb980a1ce9c225","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2012-06-23T19:24:41Z","title_canon_sha256":"ef2e4ff48505da881e8aabf1cc830811de4631b854fcf118aa081cdf7f13a2f0"},"schema_version":"1.0","source":{"id":"1206.5433","kind":"arxiv","version":1}},"canonical_sha256":"c5c116a0fc7c144c8673feb12528de4be5ae7e571be20956c76b5a5955e31910","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5c116a0fc7c144c8673feb12528de4be5ae7e571be20956c76b5a5955e31910","first_computed_at":"2026-05-18T00:10:19.846740Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:19.846740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QlL/xRLqQL6HmKRCrwkofzeXkMRcKcmiYtdUUB/ymgtDqigk4V7IoA3Mdks/WYaJkdPE0AIyA63GnUO14l5fCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:19.847174Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5433","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01ac83bd3c8e71c19015efb8a9a2c42e4d95115bc96ae44ee9f9c3ee8743bf36","sha256:cc7fd2480e029a91aac68273dfe91c72eebfc3b9936638a9ea97b04a0edca220"],"state_sha256":"60a097d675c41c10dafc2707660da7ec03e256d059bdb062636403a1fa5fb2e1"}