{"paper":{"title":"Large values of $L(1,\\chi)$ for $k$-th order characters $\\chi$ and applications to character sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Youness Lamzouri","submitted_at":"2015-03-24T20:47:23Z","abstract_excerpt":"For any given integer $k\\geq 2$ we prove the existence of infinitely many $q$ and characters $ \\chi\\pmod q$ of order $k$, such that $|L(1,\\chi)|\\geq (e^{\\gamma}+o(1))\\log\\log q$. We believe this bound to be best possible. When the order $k$ is even, we obtain similar results for $L(1,\\chi)$ and $L(1,\\chi\\xi)$ where $\\chi$ is restricted to even (or odd) characters of order $k$, and $\\xi$ is a fixed quadratic character. As an application of these results, we exhibit large even order character sums, which are likely to be optimal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07196","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"}