{"paper":{"title":"From a cotangent sum to a generalized totient function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Michael Th. Rassias","submitted_at":"2017-05-28T09:34:47Z","abstract_excerpt":"In this paper we investigate a certain category of cotangent sums and more specifically the sum\n  $$\\sum_{m=1}^{b-1}\\cot\\left(\\frac{\\pi m}{b}\\right)\\sin^{3}\\left(2\\pi m\\frac{a}{b}\\right)\\:$$ and associate the distribution of its values to a generalized totient function $\\phi(n,A,B)$, where $$\\phi(n,A,B):=\\sum_{\\substack{A\\leq k \\leq B \\\\ (n,k)=1}}1\\:.$$ One of the methods used consists in the exploitation of relations between trigonometric sums and the fractional part of a real number."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09917","kind":"arxiv","version":2},"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"}