{"paper":{"title":"Pointwise convergence of polynomial multiple ergodic averages along the primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.NT"],"primary_cat":"math.DS","authors_text":"James Wright, Mariusz Mirek, Renhui Wan","submitted_at":"2025-05-21T14:12:38Z","abstract_excerpt":"We establish pointwise almost everywhere convergence for the polynomial multilinear ergodic averages $$\\frac{1}{N} \\sum_{n=1}^N \\La(n) f_1(T^{P_1(n)} x)\\cdots f_k(T^{P_k(n)} x)$$ as $N\\to \\infty$, where $\\La$ is the von Mangoldt function, $T \\colon X \\to X$ is an invertible measure-preserving transformation of a probability space $(X,\\nu)$, $P_1,\\ldots, P_k$ are polynomials with integer coefficients and distinct degrees, and $f_1,\\ldots,f_k\\in L^\\infty(X)$. This pointwise almost everywhere convergence result can be seen as a refinement of the norm convergence result obtained in Wooley--Ziegler"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.15549","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/2505.15549/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"}