{"paper":{"title":"On the distribution of a cotangent sum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Sandro Bettin","submitted_at":"2014-11-09T22:47:19Z","abstract_excerpt":"Maier and Rassias computed the moments and proved a distribution result for the cotangent sum $c_0(a/q):=-\\sum_{m<q}\\frac mq\\cot(\\frac{\\pi ma}{q})$ on average over $1/2<A_0\\leq a/q<A_1<1$, as $q\\rightarrow \\infty$. We give a simple argument that recovers their results (with stronger error terms) and extends them to the full range $1\\leq a<q$. Moreover, we give a density result for $c_0$ and answer a question posed by Maier and Rassias on the growth of the moments of $c_0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2293","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"}