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This pointwise almost everywhere convergence result can be seen as a refinement of the norm convergence result obtained in Wooley--Ziegler"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2505.15549","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-05-21T14:12:38Z","cross_cats_sorted":["math.CA","math.NT"],"title_canon_sha256":"82e12778e7999291af1b553e4de5e2ecbd99f64b1c5c6597f55376fbeca850cd","abstract_canon_sha256":"7110b4352d2be03531059f127d5504f952963d9f337f01cdf437c981612594d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T03:13:45.534910Z","signature_b64":"sRd5n9nsklErXgF2prwiwwH+6m8Q9eOlSp9ha3IIiotkprEYGRYMyO3qgUxqwgDxK4ouU4aa17flMqvfwTpVAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"644a2be780d258105cd4b629f75cfafcf5ee4ed5a50a94979ed04f1a0ecd55f8","last_reissued_at":"2026-06-23T03:13:45.534422Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T03:13:45.534422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $f_1,\\ldots,f_k\\in L^\\infty(X)$. 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