{"paper":{"title":"Exact Kronecker Constants of Three Element Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CA","authors_text":"Kathryn E. Hare, L. Thomas Ramsey","submitted_at":"2015-03-26T20:33:35Z","abstract_excerpt":"For any three element set of positive integers, $\\{a,b,n\\}$, with $a<b<n$, $n$ sufficiently large and $\\gcd(a,b)=1$, we find the least $\\alpha$ such that given any real numbers $t_1$, $t_2$, $t_3$, there is a real number $x$ such that \\begin{equation*} \\max \\{\\left\\langle ax-t_{1}\\right\\rangle ,\\left\\langle bx-t_{2}\\right\\rangle ,\\left\\langle nx-t_{3}\\right\\rangle \\}\\leq \\alpha , \\end{equation*} where $\\left\\langle \\cdot \\right\\rangle $ denotes the distance to the nearest integer. The number $\\alpha $ is known as the angular Kronecker constant of $\\{a,b,n\\}$. We also find the least $\\beta $ su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.09071","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"}