{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:XBYSFLL4UWUSMYFOBF2JMQEJH5","short_pith_number":"pith:XBYSFLL4","schema_version":"1.0","canonical_sha256":"b87122ad7ca5a92660ae09749640893f4649862aaed724cafb6be6f065fbdead","source":{"kind":"arxiv","id":"1602.02326","version":1},"attestation_state":"computed","paper":{"title":"Epstein zeta-functions, subconvexity, and the purity conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Valentin Blomer","submitted_at":"2016-02-07T01:11:43Z","abstract_excerpt":"Subconvexity bounds are proved for general Epstein zeta functions of k-ary quadratic forms. This is related to sup-norm bounds for Eisenstein series on GL(k), and the exact sup-norm exponent is determined to be (k-2)/8 for k >= 2. In particular, if $k$ is odd, this exponent is not in Z/4, which shows that Sarnak's purity conjecture does not hold for Eisenstein series."},"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":"1602.02326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-07T01:11:43Z","cross_cats_sorted":[],"title_canon_sha256":"4c44bfbd90bc08122ca769b698f7721bd350216bf228dd78dbf314bf113b6743","abstract_canon_sha256":"0646d1e251984ed937cf3cc1aad48d1c8d42f220391a7632ff9c4066dfaf4af9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:10.303455Z","signature_b64":"jsHEKzUHsWukpMLR0v5nSfnJhJbYM2SAg9WnE3MvJIRdz5biHxAjhlbSkC47uRLGvcK9ELWTAN4eKj5cGlheDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b87122ad7ca5a92660ae09749640893f4649862aaed724cafb6be6f065fbdead","last_reissued_at":"2026-05-18T01:21:10.302670Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:10.302670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Epstein zeta-functions, subconvexity, and the purity conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Valentin Blomer","submitted_at":"2016-02-07T01:11:43Z","abstract_excerpt":"Subconvexity bounds are proved for general Epstein zeta functions of k-ary quadratic forms. This is related to sup-norm bounds for Eisenstein series on GL(k), and the exact sup-norm exponent is determined to be (k-2)/8 for k >= 2. In particular, if $k$ is odd, this exponent is not in Z/4, which shows that Sarnak's purity conjecture does not hold for Eisenstein series."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02326","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":"1602.02326","created_at":"2026-05-18T01:21:10.302789+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.02326v1","created_at":"2026-05-18T01:21:10.302789+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02326","created_at":"2026-05-18T01:21:10.302789+00:00"},{"alias_kind":"pith_short_12","alias_value":"XBYSFLL4UWUS","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XBYSFLL4UWUSMYFO","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XBYSFLL4","created_at":"2026-05-18T12:30:51.357362+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/XBYSFLL4UWUSMYFOBF2JMQEJH5","json":"https://pith.science/pith/XBYSFLL4UWUSMYFOBF2JMQEJH5.json","graph_json":"https://pith.science/api/pith-number/XBYSFLL4UWUSMYFOBF2JMQEJH5/graph.json","events_json":"https://pith.science/api/pith-number/XBYSFLL4UWUSMYFOBF2JMQEJH5/events.json","paper":"https://pith.science/paper/XBYSFLL4"},"agent_actions":{"view_html":"https://pith.science/pith/XBYSFLL4UWUSMYFOBF2JMQEJH5","download_json":"https://pith.science/pith/XBYSFLL4UWUSMYFOBF2JMQEJH5.json","view_paper":"https://pith.science/paper/XBYSFLL4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.02326&json=true","fetch_graph":"https://pith.science/api/pith-number/XBYSFLL4UWUSMYFOBF2JMQEJH5/graph.json","fetch_events":"https://pith.science/api/pith-number/XBYSFLL4UWUSMYFOBF2JMQEJH5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XBYSFLL4UWUSMYFOBF2JMQEJH5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XBYSFLL4UWUSMYFOBF2JMQEJH5/action/storage_attestation","attest_author":"https://pith.science/pith/XBYSFLL4UWUSMYFOBF2JMQEJH5/action/author_attestation","sign_citation":"https://pith.science/pith/XBYSFLL4UWUSMYFOBF2JMQEJH5/action/citation_signature","submit_replication":"https://pith.science/pith/XBYSFLL4UWUSMYFOBF2JMQEJH5/action/replication_record"}},"created_at":"2026-05-18T01:21:10.302789+00:00","updated_at":"2026-05-18T01:21:10.302789+00:00"}