{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MBHGKDQ2DM4ZPHKHZ2UNQA45RE","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":"68f6958c50bdd35b6be81e058619450cc2aad97825f5ba98d623dcaf7fade6c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-22T19:01:35Z","title_canon_sha256":"38c1087b438c5b9990625065d410826680458afd7d0ea3c2b43f03dff8c28d32"},"schema_version":"1.0","source":{"id":"1512.07204","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07204","created_at":"2026-05-17T23:39:28Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07204v6","created_at":"2026-05-17T23:39:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07204","created_at":"2026-05-17T23:39:28Z"},{"alias_kind":"pith_short_12","alias_value":"MBHGKDQ2DM4Z","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MBHGKDQ2DM4ZPHKH","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MBHGKDQ2","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:459954016346f80dd6028377794775f7c2cbe90e6c43d7cfbe0a4ac22258372c","target":"graph","created_at":"2026-05-17T23:39:28Z","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 formulate an explicit refinement of B\\\"ocherer's conjecture for Siegel modular forms of degree 2 and squarefree level, relating weighted averages of Fourier coefficients with special values of L-functions. To achieve this, we compute the relevant local integrals that appear in the refined global Gan-Gross-Prasad conjecture for Bessel periods as proposed by Yifeng Liu. We note several consequences of our conjecture to arithmetic and analytic properties of L-functions and Fourier coefficients of Siegel modular forms.","authors_text":"Abhishek Saha, Ameya Pitale, Martin Dickson, Ralf Schmidt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-22T19:01:35Z","title":"Explicit refinements of B\\\"ocherer's conjecture for Siegel modular forms of squarefree level"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07204","kind":"arxiv","version":6},"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":"sha256:0f6f0ccdb9d90cdcbc5bfff9cfb8d4e752600e5a32b00e1eb5c7e88691e1ce73","target":"record","created_at":"2026-05-17T23:39:28Z","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":"68f6958c50bdd35b6be81e058619450cc2aad97825f5ba98d623dcaf7fade6c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-22T19:01:35Z","title_canon_sha256":"38c1087b438c5b9990625065d410826680458afd7d0ea3c2b43f03dff8c28d32"},"schema_version":"1.0","source":{"id":"1512.07204","kind":"arxiv","version":6}},"canonical_sha256":"604e650e1a1b39979d47cea8d8039d891e3c87f3f667007d32f1dea7ec77eb1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"604e650e1a1b39979d47cea8d8039d891e3c87f3f667007d32f1dea7ec77eb1a","first_computed_at":"2026-05-17T23:39:28.017937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:28.017937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KSvWivl3i8ggMYvJGtUkvyo9Pr4/aEHk9U2/TQaTZoLEJ8ZaD43O5E2r6nRf2HsJWIRWL2RqWnry722l5BPwBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:28.018566Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.07204","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f6f0ccdb9d90cdcbc5bfff9cfb8d4e752600e5a32b00e1eb5c7e88691e1ce73","sha256:459954016346f80dd6028377794775f7c2cbe90e6c43d7cfbe0a4ac22258372c"],"state_sha256":"a676ac795d52fef307873e849179d3247e55a2b1950808045b383cbde2fd03e4"}