{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:D5NL3SHRRYWORXTENCB6XYXS3S","short_pith_number":"pith:D5NL3SHR","schema_version":"1.0","canonical_sha256":"1f5abdc8f18e2ce8de646883ebe2f2dca616b431753f1dd33d2ab0e84ba8c5ce","source":{"kind":"arxiv","id":"math/0412063","version":3},"attestation_state":"computed","paper":{"title":"Incomplete Quadratic Exponential Sums in Several Variables","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Amitabha Roy, Eduardo Duenez, Howard Straubing, Steven J. Miller","submitted_at":"2004-12-02T21:30:06Z","abstract_excerpt":"We consider incomplete exponential sums in several variables of the form S(f,n,m) = \\frac{1}{2^n} \\sum_{x_1 \\in \\{-1,1\\}} ... \\sum_{x_n \\in \\{-1,1\\}} x_1 ... x_n e^{2\\pi i f(x)/p}, where m>1 is odd and f is a polynomial of degree d with coefficients in Z/mZ. We investigate the conjecture, originating in a problem in computational complexity, that for each fixed d and m the maximum norm of S(f,n,m) converges exponentially fast to 0 as n grows to infinity. The conjecture is known to hold in the case when m=3 and d=2, but existing methods for studying incomplete exponential sums appear to be insu"},"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":"math/0412063","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2004-12-02T21:30:06Z","cross_cats_sorted":[],"title_canon_sha256":"0b5bb0efa346bf10cf0b33a5ff8c907111c514bca42abdeb90dd70ffd67bbd57","abstract_canon_sha256":"c0931a46c152654ebdd86e842502a0f88086ace0fd3ec89049bf6e4946e535f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:55.537919Z","signature_b64":"pJ7JQc38dUIlsxgvq5w8szjJMNn+kjSn2h7i7t+6kkdtwsnqx8I6M1pp7ha6apvWAa64CTw0Vpog6hgpVPQZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f5abdc8f18e2ce8de646883ebe2f2dca616b431753f1dd33d2ab0e84ba8c5ce","last_reissued_at":"2026-05-18T04:35:55.537357Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:55.537357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Incomplete Quadratic Exponential Sums in Several Variables","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Amitabha Roy, Eduardo Duenez, Howard Straubing, Steven J. Miller","submitted_at":"2004-12-02T21:30:06Z","abstract_excerpt":"We consider incomplete exponential sums in several variables of the form S(f,n,m) = \\frac{1}{2^n} \\sum_{x_1 \\in \\{-1,1\\}} ... \\sum_{x_n \\in \\{-1,1\\}} x_1 ... x_n e^{2\\pi i f(x)/p}, where m>1 is odd and f is a polynomial of degree d with coefficients in Z/mZ. We investigate the conjecture, originating in a problem in computational complexity, that for each fixed d and m the maximum norm of S(f,n,m) converges exponentially fast to 0 as n grows to infinity. The conjecture is known to hold in the case when m=3 and d=2, but existing methods for studying incomplete exponential sums appear to be insu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0412063","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":"math/0412063","created_at":"2026-05-18T04:35:55.537417+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0412063v3","created_at":"2026-05-18T04:35:55.537417+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0412063","created_at":"2026-05-18T04:35:55.537417+00:00"},{"alias_kind":"pith_short_12","alias_value":"D5NL3SHRRYWO","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"D5NL3SHRRYWORXTE","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"D5NL3SHR","created_at":"2026-05-18T12:25:52.687210+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/D5NL3SHRRYWORXTENCB6XYXS3S","json":"https://pith.science/pith/D5NL3SHRRYWORXTENCB6XYXS3S.json","graph_json":"https://pith.science/api/pith-number/D5NL3SHRRYWORXTENCB6XYXS3S/graph.json","events_json":"https://pith.science/api/pith-number/D5NL3SHRRYWORXTENCB6XYXS3S/events.json","paper":"https://pith.science/paper/D5NL3SHR"},"agent_actions":{"view_html":"https://pith.science/pith/D5NL3SHRRYWORXTENCB6XYXS3S","download_json":"https://pith.science/pith/D5NL3SHRRYWORXTENCB6XYXS3S.json","view_paper":"https://pith.science/paper/D5NL3SHR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0412063&json=true","fetch_graph":"https://pith.science/api/pith-number/D5NL3SHRRYWORXTENCB6XYXS3S/graph.json","fetch_events":"https://pith.science/api/pith-number/D5NL3SHRRYWORXTENCB6XYXS3S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D5NL3SHRRYWORXTENCB6XYXS3S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D5NL3SHRRYWORXTENCB6XYXS3S/action/storage_attestation","attest_author":"https://pith.science/pith/D5NL3SHRRYWORXTENCB6XYXS3S/action/author_attestation","sign_citation":"https://pith.science/pith/D5NL3SHRRYWORXTENCB6XYXS3S/action/citation_signature","submit_replication":"https://pith.science/pith/D5NL3SHRRYWORXTENCB6XYXS3S/action/replication_record"}},"created_at":"2026-05-18T04:35:55.537417+00:00","updated_at":"2026-05-18T04:35:55.537417+00:00"}