{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:PUVJZEA4W5WU7N762SETVF2UUN","short_pith_number":"pith:PUVJZEA4","schema_version":"1.0","canonical_sha256":"7d2a9c901cb76d4fb7fed4893a9754a37c8d79def7e921ea9558c4ff343e4fd2","source":{"kind":"arxiv","id":"1510.02925","version":1},"attestation_state":"computed","paper":{"title":"Estimates of Hilbert modular cusp forms of half-integral and integral weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anilatmaja Aryasomayajula","submitted_at":"2015-10-10T13:31:35Z","abstract_excerpt":"Let $\\Gamma$ be a cocompact, discrete, and irreducible subgroup of $\\mathrm{PSL}_{2}(\\mathbb{R})^{n}$. Let $\\nu$ be a unitary character of $\\Gamma$. For $k\\in1\\slash 2\\,\\mathbb{Z}$, let $\\sknu$ denote the complex vector space of cusp forms of weight-$\\tk=\\k$ and nebentypus $\\nu^{2k}$ with respect to $\\Gamma$. We assume that $\\omega_{X,\\nu}$, the line bundle of cusp forms of weight-$\\tilde{1\\slash 2}:=(1\\slash 2,\\ldots,1\\slash2)$ with nebentypus $\\nu$ over $X$ exists. Let $\\lbrace f_{1},\\ldots,f_{j_{\\tk}} \\rbrace$ denote an orthonormal basis of $\\sknu$. In this article, we show that as $k\\right"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1510.02925","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-10T13:31:35Z","cross_cats_sorted":[],"title_canon_sha256":"f1ab832ea4a4b09d867e61ce7bb83024c4520bc071d672a91c42bb61d3a27912","abstract_canon_sha256":"0da8052fa213910833360b5f3d6a567305ffe9858cbda8d600248c1e79533dd7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:33.346305Z","signature_b64":"oO4pkgqVhUMWhoDFohzvPx5jULXRfNMi96VcZPCTpz4uzBcTdyLt+JBaYw7zqupoBJ/5xQxzNGcmH/cZvjxEAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d2a9c901cb76d4fb7fed4893a9754a37c8d79def7e921ea9558c4ff343e4fd2","last_reissued_at":"2026-05-18T01:30:33.345774Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:33.345774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Estimates of Hilbert modular cusp forms of half-integral and integral weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anilatmaja Aryasomayajula","submitted_at":"2015-10-10T13:31:35Z","abstract_excerpt":"Let $\\Gamma$ be a cocompact, discrete, and irreducible subgroup of $\\mathrm{PSL}_{2}(\\mathbb{R})^{n}$. Let $\\nu$ be a unitary character of $\\Gamma$. For $k\\in1\\slash 2\\,\\mathbb{Z}$, let $\\sknu$ denote the complex vector space of cusp forms of weight-$\\tk=\\k$ and nebentypus $\\nu^{2k}$ with respect to $\\Gamma$. We assume that $\\omega_{X,\\nu}$, the line bundle of cusp forms of weight-$\\tilde{1\\slash 2}:=(1\\slash 2,\\ldots,1\\slash2)$ with nebentypus $\\nu$ over $X$ exists. Let $\\lbrace f_{1},\\ldots,f_{j_{\\tk}} \\rbrace$ denote an orthonormal basis of $\\sknu$. In this article, we show that as $k\\right"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02925","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1510.02925","created_at":"2026-05-18T01:30:33.345849+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.02925v1","created_at":"2026-05-18T01:30:33.345849+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02925","created_at":"2026-05-18T01:30:33.345849+00:00"},{"alias_kind":"pith_short_12","alias_value":"PUVJZEA4W5WU","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"PUVJZEA4W5WU7N76","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"PUVJZEA4","created_at":"2026-05-18T12:29:37.295048+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PUVJZEA4W5WU7N762SETVF2UUN","json":"https://pith.science/pith/PUVJZEA4W5WU7N762SETVF2UUN.json","graph_json":"https://pith.science/api/pith-number/PUVJZEA4W5WU7N762SETVF2UUN/graph.json","events_json":"https://pith.science/api/pith-number/PUVJZEA4W5WU7N762SETVF2UUN/events.json","paper":"https://pith.science/paper/PUVJZEA4"},"agent_actions":{"view_html":"https://pith.science/pith/PUVJZEA4W5WU7N762SETVF2UUN","download_json":"https://pith.science/pith/PUVJZEA4W5WU7N762SETVF2UUN.json","view_paper":"https://pith.science/paper/PUVJZEA4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.02925&json=true","fetch_graph":"https://pith.science/api/pith-number/PUVJZEA4W5WU7N762SETVF2UUN/graph.json","fetch_events":"https://pith.science/api/pith-number/PUVJZEA4W5WU7N762SETVF2UUN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PUVJZEA4W5WU7N762SETVF2UUN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PUVJZEA4W5WU7N762SETVF2UUN/action/storage_attestation","attest_author":"https://pith.science/pith/PUVJZEA4W5WU7N762SETVF2UUN/action/author_attestation","sign_citation":"https://pith.science/pith/PUVJZEA4W5WU7N762SETVF2UUN/action/citation_signature","submit_replication":"https://pith.science/pith/PUVJZEA4W5WU7N762SETVF2UUN/action/replication_record"}},"created_at":"2026-05-18T01:30:33.345849+00:00","updated_at":"2026-05-18T01:30:33.345849+00:00"}