{"paper":{"title":"Approximate orthogonality of powers for ergodic affine unipotent diffeomorphisms on nilmanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Joanna Ku{\\l}aga-Przymus, Krzysztof Fr\\k{a}czek, Livio Flaminio, Mariusz Lema\\'nczyk","submitted_at":"2016-09-02T18:56:00Z","abstract_excerpt":"Let $ G $ be a connected, simply connected nilpotent Lie group and $ \\Gamma < G $ a lattice. We prove that each ergodic diffeomorphism $ \\phi(x\\Gamma)=uA(x)\\Gamma $ on the nilmanifold $ G/\\Gamma $, where $ u\\in G $ and $ A:G\\to G $ is a unipotent automorphism satisfying $ A(\\Gamma)=\\Gamma $, enjoys the property of asymptotically orthogonal powers (AOP). Two consequences follow:\n  (i) Sarnak's conjecture on M\\\"obius orthogonality holds in every uniquely ergodic model of an ergodic affine unipotent diffeomorphism;\n  (ii) For ergodic affine unipotent diffeomorphisms themselves, the M\\\"obius ortho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00699","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"}