{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:YX2M3HFUOMCPM6XFFLXKEDKDLQ","short_pith_number":"pith:YX2M3HFU","schema_version":"1.0","canonical_sha256":"c5f4cd9cb47304f67ae52aeea20d435c1118a65732ba83af57be19cb1b3ab285","source":{"kind":"arxiv","id":"0808.1756","version":3},"attestation_state":"computed","paper":{"title":"On Hecke Eigenvalues at Piatetski-Shapiro Primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Liangyi Zhao, Stephan Baier","submitted_at":"2008-08-12T23:32:55Z","abstract_excerpt":"Let $\\lambda(n)$ be the normalized n-th Fourier coefficient of a holomorphic cusp form for the full modular group. We show that for some constant $C > 0$ depending on the cusp form and every fixed $c$ in the range $1 < c < 8/7$, the mean value of $\\lambda(p)$ is $\\ll \\exp (-C \\sqrt{\\log N})$ as p runs over all (Piatetski-Shapiro) primes of the form $[n^c]$ with a natural number $n \\leq N$."},"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":"0808.1756","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-08-12T23:32:55Z","cross_cats_sorted":[],"title_canon_sha256":"dc2f8018e7c0589f39aca9e59d5f4aec8c8c2e7c414668fab83b639e365766de","abstract_canon_sha256":"bd26e9142bdbd32b93a926e2e2d2d3c2f559bda918751a7e1e93c94b4d2a5ee9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:11.250542Z","signature_b64":"q/idEYbtO/hZBzBAuppIFvPQlYMEQot2GOL4rs6KnqD6fAFL0cHChXH588IbHaQkDf8NzwEgTrofdfzuTIBpBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5f4cd9cb47304f67ae52aeea20d435c1118a65732ba83af57be19cb1b3ab285","last_reissued_at":"2026-05-18T02:58:11.250038Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:11.250038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Hecke Eigenvalues at Piatetski-Shapiro Primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Liangyi Zhao, Stephan Baier","submitted_at":"2008-08-12T23:32:55Z","abstract_excerpt":"Let $\\lambda(n)$ be the normalized n-th Fourier coefficient of a holomorphic cusp form for the full modular group. We show that for some constant $C > 0$ depending on the cusp form and every fixed $c$ in the range $1 < c < 8/7$, the mean value of $\\lambda(p)$ is $\\ll \\exp (-C \\sqrt{\\log N})$ as p runs over all (Piatetski-Shapiro) primes of the form $[n^c]$ with a natural number $n \\leq N$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.1756","kind":"arxiv","version":3},"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":"0808.1756","created_at":"2026-05-18T02:58:11.250104+00:00"},{"alias_kind":"arxiv_version","alias_value":"0808.1756v3","created_at":"2026-05-18T02:58:11.250104+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.1756","created_at":"2026-05-18T02:58:11.250104+00:00"},{"alias_kind":"pith_short_12","alias_value":"YX2M3HFUOMCP","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"YX2M3HFUOMCPM6XF","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"YX2M3HFU","created_at":"2026-05-18T12:25:58.018023+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/YX2M3HFUOMCPM6XFFLXKEDKDLQ","json":"https://pith.science/pith/YX2M3HFUOMCPM6XFFLXKEDKDLQ.json","graph_json":"https://pith.science/api/pith-number/YX2M3HFUOMCPM6XFFLXKEDKDLQ/graph.json","events_json":"https://pith.science/api/pith-number/YX2M3HFUOMCPM6XFFLXKEDKDLQ/events.json","paper":"https://pith.science/paper/YX2M3HFU"},"agent_actions":{"view_html":"https://pith.science/pith/YX2M3HFUOMCPM6XFFLXKEDKDLQ","download_json":"https://pith.science/pith/YX2M3HFUOMCPM6XFFLXKEDKDLQ.json","view_paper":"https://pith.science/paper/YX2M3HFU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0808.1756&json=true","fetch_graph":"https://pith.science/api/pith-number/YX2M3HFUOMCPM6XFFLXKEDKDLQ/graph.json","fetch_events":"https://pith.science/api/pith-number/YX2M3HFUOMCPM6XFFLXKEDKDLQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YX2M3HFUOMCPM6XFFLXKEDKDLQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YX2M3HFUOMCPM6XFFLXKEDKDLQ/action/storage_attestation","attest_author":"https://pith.science/pith/YX2M3HFUOMCPM6XFFLXKEDKDLQ/action/author_attestation","sign_citation":"https://pith.science/pith/YX2M3HFUOMCPM6XFFLXKEDKDLQ/action/citation_signature","submit_replication":"https://pith.science/pith/YX2M3HFUOMCPM6XFFLXKEDKDLQ/action/replication_record"}},"created_at":"2026-05-18T02:58:11.250104+00:00","updated_at":"2026-05-18T02:58:11.250104+00:00"}