{"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"}