{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ZE54MO5CCCNUBV6EASDFF26J7Z","short_pith_number":"pith:ZE54MO5C","schema_version":"1.0","canonical_sha256":"c93bc63ba2109b40d7c4048652ebc9fe71390141203ea6f16a9f64306f76508f","source":{"kind":"arxiv","id":"1502.00769","version":1},"attestation_state":"computed","paper":{"title":"Trilinear forms with Kloosterman fractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Sandro Bettin, Vorrapan Chandee","submitted_at":"2015-02-03T07:57:21Z","abstract_excerpt":"We give new bounds for $\\sum_{{a, m ,n}}\\alpha_{m}\\beta_n\\nu_a {\\textrm e}\\left(\\frac{a\\overline m}{n}\\right)$ where $\\alpha_{m}$, $\\beta_n$ and $\\nu_a$ are arbitrary coefficients, improving upon a result of Duke, Friedlander and Iwaniec [DFI97]. We also apply these bounds to problems on representations by determinant equations and on the equidistribution of solutions to linear equations."},"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":"1502.00769","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-03T07:57:21Z","cross_cats_sorted":[],"title_canon_sha256":"839706935efbe6c3b0eee54fa9c39a1e103752c1552b92a6d63a5a71c544a0d2","abstract_canon_sha256":"ddfe03570272fa123a51166e86cbdfb2e449363769fb8f93292b970ed69dff5f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:52.679964Z","signature_b64":"TBLz2i1dEf0qJ/DxgWoKXl+CPtWb5pn5dy/b4C6DGNFwLDrz85i2XpC9GrvMcWkzJG+Xg5bPT6nJlMgIcJTeDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c93bc63ba2109b40d7c4048652ebc9fe71390141203ea6f16a9f64306f76508f","last_reissued_at":"2026-05-18T00:20:52.677957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:52.677957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Trilinear forms with Kloosterman fractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Sandro Bettin, Vorrapan Chandee","submitted_at":"2015-02-03T07:57:21Z","abstract_excerpt":"We give new bounds for $\\sum_{{a, m ,n}}\\alpha_{m}\\beta_n\\nu_a {\\textrm e}\\left(\\frac{a\\overline m}{n}\\right)$ where $\\alpha_{m}$, $\\beta_n$ and $\\nu_a$ are arbitrary coefficients, improving upon a result of Duke, Friedlander and Iwaniec [DFI97]. We also apply these bounds to problems on representations by determinant equations and on the equidistribution of solutions to linear equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00769","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":"1502.00769","created_at":"2026-05-18T00:20:52.679535+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.00769v1","created_at":"2026-05-18T00:20:52.679535+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00769","created_at":"2026-05-18T00:20:52.679535+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZE54MO5CCCNU","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZE54MO5CCCNUBV6E","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZE54MO5C","created_at":"2026-05-18T12:29:52.810259+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/ZE54MO5CCCNUBV6EASDFF26J7Z","json":"https://pith.science/pith/ZE54MO5CCCNUBV6EASDFF26J7Z.json","graph_json":"https://pith.science/api/pith-number/ZE54MO5CCCNUBV6EASDFF26J7Z/graph.json","events_json":"https://pith.science/api/pith-number/ZE54MO5CCCNUBV6EASDFF26J7Z/events.json","paper":"https://pith.science/paper/ZE54MO5C"},"agent_actions":{"view_html":"https://pith.science/pith/ZE54MO5CCCNUBV6EASDFF26J7Z","download_json":"https://pith.science/pith/ZE54MO5CCCNUBV6EASDFF26J7Z.json","view_paper":"https://pith.science/paper/ZE54MO5C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.00769&json=true","fetch_graph":"https://pith.science/api/pith-number/ZE54MO5CCCNUBV6EASDFF26J7Z/graph.json","fetch_events":"https://pith.science/api/pith-number/ZE54MO5CCCNUBV6EASDFF26J7Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZE54MO5CCCNUBV6EASDFF26J7Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZE54MO5CCCNUBV6EASDFF26J7Z/action/storage_attestation","attest_author":"https://pith.science/pith/ZE54MO5CCCNUBV6EASDFF26J7Z/action/author_attestation","sign_citation":"https://pith.science/pith/ZE54MO5CCCNUBV6EASDFF26J7Z/action/citation_signature","submit_replication":"https://pith.science/pith/ZE54MO5CCCNUBV6EASDFF26J7Z/action/replication_record"}},"created_at":"2026-05-18T00:20:52.679535+00:00","updated_at":"2026-05-18T00:20:52.679535+00:00"}