{"paper":{"title":"Topological correspondence of multiple ergodic averages of nilpotent group actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Song Shao, Wen Huang, Xiangdong Ye","submitted_at":"2016-04-25T02:42:45Z","abstract_excerpt":"Let $(X,\\Gamma)$ be a topological system, where $\\Gamma$ is a nilpotent group generated by $T_1,\\ldots, T_d$ such that for each $T\\in \\Gamma$, $T\\neq e_\\Gamma$, $(X,T)$ is weakly mixing and minimal. For $d,k\\in \\mathbb{N}$, let $p_{i,j}(n), 1\\le i\\le k, 1\\le j\\le d$ be polynomials with rational coefficients taking integer values on the integers and $p_{i,j}(0)=0$. We show that if the expressions $g_i(n)=T_1^{p_{i,1}(n)}\\cdots T_d^{p_{i,d}(n)}$ depends nontrivially on $n$ for $i=1,2,\\cdots,k$, and for all $i\\neq j\\in \\{1,2,\\ldots,k\\}$ the expressions $g_i(n)g_j(n)^{-1}$ depend nontrivially on $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07113","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"}