{"paper":{"title":"Averages of character sums","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jonathan Bober","submitted_at":"2014-09-05T15:39:05Z","abstract_excerpt":"We show that a short truncation of the Fourier expansion for a character sum gives a good approximation for the average value of that character sum over an interval.\n  We give a few applications of this result. One is that for any $b$ there are infinitely many characters for which the sum up to $\\approx aq/b$ is $\\gg q^{1/2} \\log \\log q$ for all $a$ relatively prime to $b$; another is that if the least quadratic nonresidue modulo $q \\equiv 3 \\pmod 4$ is large, then the character sum gets as large as $(\\sqrt{q}/\\pi) (L(1, \\chi) + \\log 2 - \\epsilon)$, and if $B$ is this nonresidue, then there is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1840","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"}