{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:4ZHMK243RKEEF3CX3IGVDMM35V","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":"5bdd809f88bfa50bc18c9282482dc0aacacc071568b45f7e78f48640694bd6bf","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-10-13T19:49:35Z","title_canon_sha256":"9abdd409208af1e1051febf770a00d51e152d70e21f6beb924dee6cc418f6ebc"},"schema_version":"1.0","source":{"id":"0810.2292","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.2292","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"arxiv_version","alias_value":"0810.2292v4","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.2292","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"pith_short_12","alias_value":"4ZHMK243RKEE","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"4ZHMK243RKEEF3CX","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"4ZHMK243","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:408d9773e0fb8f0e186104825208e14d1979b0f4e4248510db0aad96c00bda83","target":"graph","created_at":"2026-05-18T02:58:11Z","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":"We prove several results on the distribution of values of $L$-functions at the edge of the critical strip, by constructing and studying a large class of random Euler products. Among new applications, we study families of symmetric power $L$-functions of holomorphic cusp forms in the level aspect (assuming the automorphy of these $L$-functions) at $s=1$, functions in the Selberg class (in the height aspect), and quadratic twists of a fixed $GL(m)/{\\Bbb Q}$-automorphic cusp form at $s=1$.","authors_text":"Youness Lamzouri","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-10-13T19:49:35Z","title":"Distribution of values of $L$-functions at the edge of the critical strip"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.2292","kind":"arxiv","version":4},"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":"sha256:08afc3b9e3fca2229e01684f47a54dd81ddb7e4b54f1b9099413be7117baac5b","target":"record","created_at":"2026-05-18T02:58:11Z","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":"5bdd809f88bfa50bc18c9282482dc0aacacc071568b45f7e78f48640694bd6bf","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-10-13T19:49:35Z","title_canon_sha256":"9abdd409208af1e1051febf770a00d51e152d70e21f6beb924dee6cc418f6ebc"},"schema_version":"1.0","source":{"id":"0810.2292","kind":"arxiv","version":4}},"canonical_sha256":"e64ec56b9b8a8842ec57da0d51b19bed6a4e9be58cc8949ec8a4a6d8e06c3efd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e64ec56b9b8a8842ec57da0d51b19bed6a4e9be58cc8949ec8a4a6d8e06c3efd","first_computed_at":"2026-05-18T02:58:11.052103Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:11.052103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4QLMuPxoDUgARNb7GDe7r6y6DiLdYdYiKSOi58IAcH0OxIi5YCt7t1weQQ6+0jRGZaiQxLNNv2adMKmpWYclCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:11.052701Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.2292","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08afc3b9e3fca2229e01684f47a54dd81ddb7e4b54f1b9099413be7117baac5b","sha256:408d9773e0fb8f0e186104825208e14d1979b0f4e4248510db0aad96c00bda83"],"state_sha256":"6221afb0fbf747d6e141dd6863efa07cc0fcba91d8f31c9e1877da535c53d8d7"}