{"paper":{"title":"Cancellation in the Additive Twists of Fourier Coefficients for $\\mathrm{GL}_2$ and $\\mathrm{GL}_3$ over Number Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Zhi Qi","submitted_at":"2016-10-17T23:33:43Z","abstract_excerpt":"In this article, we study the sum of additively twisted Fourier coefficients of an irreducible cuspidal automorphic representation of $\\mathrm{GL}_2$ or $\\mathrm{GL}_3$ over an arbitrary number field. When the representation is unramified at all non-archimedean places, we prove the Wilton type bound for $\\mathrm{GL}_2$ and the Miller type bound for $\\mathrm{GL}_3$ which are uniform in terms of the additive character."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05380","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"}