{"paper":{"title":"The maximum size of short character sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Marc Munsch","submitted_at":"2018-05-18T12:12:25Z","abstract_excerpt":"In the present note, we prove new lower bounds on large values of character sums $\\Delta(x,q):=\\max_{\\chi \\neq \\chi_0} \\vert \\sum_{n\\leq x} \\chi(n)\\vert$ in certain ranges of $x$. Employing an implementation of the resonance method developed in a work involving the author in order to exhibit large values of $L$- functions, we improve some results of Hough in the range $\\log x = o(\\sqrt{\\log q})$. Our results are expressed using the counting function of $y$- friable integers less than $x$ where we improve the level of smoothness $y$ for short intervals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07163","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"}