{"paper":{"title":"Ergodic averages for sparse sequences along primes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.NT"],"primary_cat":"math.DS","authors_text":"Andreas Koutsogiannis, Konstantinos Tsinas","submitted_at":"2023-09-10T06:08:34Z","abstract_excerpt":"We investigate the limiting behavior of multiple ergodic averages along sparse sequences evaluated at prime numbers. Our sequences arise from smooth and well-behaved functions that have polynomial growth. Central to this topic is a comparison result between standard Ces\\'{a}ro averages along positive integers and averages weighted by the (modified) von Mangoldt function. The main ingredients are a recent result of Matom\\\"{a}ki, Shao, Tao and Ter\\\"{a}v\\\"{a}inen on the Gowers uniformity of the latter function in short intervals, a lifting argument that allows one to pass from actions of integers"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.04939","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.04939/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}