{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GMCFHJ4DSRK42EID6UB7THMS55","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":"cba6116c15141c94280270ebdf71225bd1f26839835665156ab1ab33239df614","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-07-25T02:24:40Z","title_canon_sha256":"07b5bc5760cf42216ebb0a8905aa1c169b35a4d8f22a1225dd500901c090e88d"},"schema_version":"1.0","source":{"id":"1707.07790","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07790","created_at":"2026-05-18T00:39:30Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07790v1","created_at":"2026-05-18T00:39:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07790","created_at":"2026-05-18T00:39:30Z"},{"alias_kind":"pith_short_12","alias_value":"GMCFHJ4DSRK4","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GMCFHJ4DSRK42EID","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GMCFHJ4D","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:7fead280f35ce4d1cb7cce4ceddb30a244d15c8d6667b29716d56349bb3c34f7","target":"graph","created_at":"2026-05-18T00:39:30Z","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 $L$ be the unique even self-dual lattice of signature $(25,1)$. The automorphism group $\\operatorname{Aut}(L)$ acts on the hyperbolic space $\\mathcal{H}^{25}$. We study a Poincar\\'e series $E(z,s)$ defined for $z$ in $\\mathcal{H}^{25}$, convergent for $\\operatorname{Re}(s) > 25$, invariant under $\\operatorname{Aut}(L)$ and having singularities along the mirrors of the reflection group of $L$. We compute the Fourier expansion of $E(z,s)$ at a \"Leech cusp\" and prove that it can be meromorphically continued to $\\operatorname{Re}(s) > 25/2$. Analytic continuation of Kloosterman sum zeta functi","authors_text":"Tathagata Basak","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-07-25T02:24:40Z","title":"A Poincar\\'e series on hyperbolic space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07790","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":"sha256:887b8231524766ca59d4bcb85c0da28891d2135509a184fc470af9069f058534","target":"record","created_at":"2026-05-18T00:39:30Z","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":"cba6116c15141c94280270ebdf71225bd1f26839835665156ab1ab33239df614","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-07-25T02:24:40Z","title_canon_sha256":"07b5bc5760cf42216ebb0a8905aa1c169b35a4d8f22a1225dd500901c090e88d"},"schema_version":"1.0","source":{"id":"1707.07790","kind":"arxiv","version":1}},"canonical_sha256":"330453a7839455cd1103f503f99d92ef6d7fdcc3fb27d514104ced1e10ad18d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"330453a7839455cd1103f503f99d92ef6d7fdcc3fb27d514104ced1e10ad18d7","first_computed_at":"2026-05-18T00:39:30.347857Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:30.347857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c6OnBQisXtI1F6qtueldgzF9sJ3bMyT6qAXcdeQdl5XWUuedzggWlLtTl44dZHUsYAedbVpsWk2fO6YCeMroCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:30.348554Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.07790","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:887b8231524766ca59d4bcb85c0da28891d2135509a184fc470af9069f058534","sha256:7fead280f35ce4d1cb7cce4ceddb30a244d15c8d6667b29716d56349bb3c34f7"],"state_sha256":"1251a8f069b82b638e2bdd35d17d100152c7cab76bb9e8b3559b313fc18ab847"}