{"paper":{"title":"Ergodic recurrence and bounded gaps between primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Hao Pan","submitted_at":"2016-08-14T15:28:13Z","abstract_excerpt":"Let $(X,B_X,\\mu,T)$ be a measure-preserving probability system with $T$ is invertible. Suppose that $A\\in B_X$ with $\\mu(A)>0$ and $\\epsilon>0$. For any $m\\geq 1$, there exist infinitely many primes $p_0,p_1,\\ldots,p_m$ with $p_0<\\cdots<p_m$ such that $$ \\mu(A\\cap T^{-(p_i-1)}A)\\geq \\mu(A)^2-\\epsilon $$ for each $0\\leq i\\leq m$ and $$ p_m-p_0<C_m, $$ where $C_m>0$ is a constant only depending on $m$, $A$ and $\\epsilon$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04111","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"}