{"paper":{"title":"A metric theory of minimal gaps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ze\\'ev Rudnick","submitted_at":"2017-10-05T08:26:12Z","abstract_excerpt":"We study the minimal gap statistic for fractional parts of sequences of the form $\\mathcal A^\\alpha = \\{\\alpha a(n)\\}$ where $\\mathcal A = \\{a(n)\\}$ is a sequence of distinct of integers. Assuming that the additive energy of the sequence is close to its minimal possible value, we show that for almost all $\\alpha$, the minimal gap $\\delta_{\\min}^\\alpha(N)=\\min\\{\\alpha a(m)-\\alpha a(n)\\bmod 1: 1\\leq m\\neq n\\leq N\\}$ is close to that of a random sequence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01911","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"}