{"paper":{"title":"The Wiener Wintner and Return Times Theorem Along the Primes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA","math.NT"],"primary_cat":"math.DS","authors_text":"Anastasios Fragkos, Ben Krause, Hamed Mousavi, Jan Fornal, Michael Lacey, Yu-Chen Sun","submitted_at":"2026-01-15T14:49:54Z","abstract_excerpt":"We prove the following Wiener-Wintner Theorem along the sequence of prime times, the first extension of the Wiener-Wintner Theorem to arithmetic sequences: for every probability space, $(X, \\nu),$ equipped with a measure-preserving transformation, $T : X \\to X,$ and every $f \\in L^p(X), 1 < p \\leq \\infty$, there exists a set of full probability, $X_f \\subset X$ with $\\nu(X_f) = 1,$ so that for all $\\omega \\in X_f$, \\[ \\frac{1}{N} \\sum_{n \\leq N} e^{ 2 \\pi i n \\theta} f(T^{p_n} \\omega) \\] converges for all $\\theta \\in [0,1]$; above, $\\{2 = p_1 < p_2 < \\dots\\}$ are an enumeration of the primes.\n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.10459","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.10459/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"}