{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:A2RCQFNH4DCZTOIV5VQIR37Y7Q","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":"8c0046b5472c89e3462abbd0615fe00658c2e9189293a8b3ff80a220b1512d6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-06-28T06:22:18Z","title_canon_sha256":"39d89d06eb99acd6bad231ab001f1f9e2b0f8a44c6e5afa4b8f8458364a70197"},"schema_version":"1.0","source":{"id":"1806.10786","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10786","created_at":"2026-05-18T00:05:38Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10786v2","created_at":"2026-05-18T00:05:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10786","created_at":"2026-05-18T00:05:38Z"},{"alias_kind":"pith_short_12","alias_value":"A2RCQFNH4DCZ","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"A2RCQFNH4DCZTOIV","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"A2RCQFNH","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:97b73d52e1ea5f4f3750208cf6184c7f7779c37264c6c804ec689492bab4ca8c","target":"graph","created_at":"2026-05-18T00:05:38Z","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":"Firstly we prove that the Voronoi formula of Miller-Schmid type applies to automorphic forms on GL(3) for the congruence subgroup $\\Gamma_0(N)$, when the conductor of the additive character in the formula is a multiple of $N$. As an application, we produce a result about the functional equation of $L$-function of the automorphic form on GL(3) twisted by Dirichlet characters. Secondly we prove that a similar formula applies to automorphic forms on GL(3) for the congruence subgroup $\\Gamma_0(N)$, when the conductor of the additive character in the formula is coprime with $N$.","authors_text":"Fan Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-06-28T06:22:18Z","title":"The Voronoi formula on GL(3) with ramification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10786","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":"sha256:5232343ae78db055c57752ba1559ddbac4e99eecd0248adf17a5f5f5e165cef4","target":"record","created_at":"2026-05-18T00:05:38Z","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":"8c0046b5472c89e3462abbd0615fe00658c2e9189293a8b3ff80a220b1512d6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-06-28T06:22:18Z","title_canon_sha256":"39d89d06eb99acd6bad231ab001f1f9e2b0f8a44c6e5afa4b8f8458364a70197"},"schema_version":"1.0","source":{"id":"1806.10786","kind":"arxiv","version":2}},"canonical_sha256":"06a22815a7e0c599b915ed6088eff8fc1811209846f634551d217ca1a5197c7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06a22815a7e0c599b915ed6088eff8fc1811209846f634551d217ca1a5197c7c","first_computed_at":"2026-05-18T00:05:38.771937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:38.771937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XV4s1Cmyjr7ifzX9saWpNNS5QyRNqgJHLg9iuSApBPfkvZoJ7AkD/nnw4zcQoJJjvCVlfG5j1/1pF7fDGUxzBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:38.772440Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.10786","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5232343ae78db055c57752ba1559ddbac4e99eecd0248adf17a5f5f5e165cef4","sha256:97b73d52e1ea5f4f3750208cf6184c7f7779c37264c6c804ec689492bab4ca8c"],"state_sha256":"122e60af46a817517e88576208815b527936521d93224c749bd51bbc80d6cbb1"}