{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ISNST4VNVDZMDBOJ4LBHVT76YM","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":"1718649ffcf370ad8cf0aa2c4f31c6dae5af1172a8ab016a76ec61997d42122c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-08T14:24:04Z","title_canon_sha256":"21219aba1eeadada5e5c167b35a459fa58ad85f1cfcef877dd50599deb0edbf4"},"schema_version":"1.0","source":{"id":"1409.2360","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2360","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2360v5","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2360","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"ISNST4VNVDZM","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"ISNST4VNVDZMDBOJ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"ISNST4VN","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:c27ad0355c4b620f7e4c2bc60f1f163564d2bd23af6058d71fe28979ae5479c4","target":"graph","created_at":"2026-05-18T00:04:24Z","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":"Let $F$ be a number field and let $\\mathbb{A}_F$ be its ring of adeles. Let $B$ be a quaternion algebra over $F$ and let $\\nu:B \\to F$ be the reduced norm. Consider the reductive monoid $M$ over $F$ whose points in an $F$-algebra $R$ are given by \\begin{align*} M(R):=\\{(\\gamma_1,\\gamma_2) \\in (B \\otimes_F R)^{2}:\\nu (\\gamma_1)=\\nu(\\gamma_2)\\}. \\end{align*} Motivated by an influential conjecture of Braverman and Kazhdan we prove a summation formula analogous to the Poisson summation formula for certain spaces of functions on the monoid. As an application, we define new zeta integrals for the Ra","authors_text":"Jayce R. Getz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-08T14:24:04Z","title":"A summation formula for the Rankin-Selberg monoid and a nonabelian trace formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2360","kind":"arxiv","version":5},"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":"sha256:07ab38449e348ce86104760b2e5b62eb7fe2778f0e9abd2d7193ca94a8ca0e42","target":"record","created_at":"2026-05-18T00:04:24Z","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":"1718649ffcf370ad8cf0aa2c4f31c6dae5af1172a8ab016a76ec61997d42122c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-08T14:24:04Z","title_canon_sha256":"21219aba1eeadada5e5c167b35a459fa58ad85f1cfcef877dd50599deb0edbf4"},"schema_version":"1.0","source":{"id":"1409.2360","kind":"arxiv","version":5}},"canonical_sha256":"449b29f2ada8f2c185c9e2c27acffec317f8d7eca5ab5cbcf1d6ab398179df89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"449b29f2ada8f2c185c9e2c27acffec317f8d7eca5ab5cbcf1d6ab398179df89","first_computed_at":"2026-05-18T00:04:24.529126Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:24.529126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qShQMpDqznmqtaXRXBJtFEE/P2+0gGvQBD9mCYolfwiq0LXOQ95oq3e3BB8KUhsPpcP2R1bvULT9W2gA2BgGCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:24.529850Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.2360","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07ab38449e348ce86104760b2e5b62eb7fe2778f0e9abd2d7193ca94a8ca0e42","sha256:c27ad0355c4b620f7e4c2bc60f1f163564d2bd23af6058d71fe28979ae5479c4"],"state_sha256":"8dea5f96c5cf9dc44dda9f15f5e2ab8b99129a6ff34855afb6f1b428c5c5e3dd"}