{"paper":{"title":"A criterion for weighted uniform distribution along functions from a Hardy field","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Michael Reilly","submitted_at":"2026-06-06T08:02:27Z","abstract_excerpt":"A classical theorem of Boshernitzan states that if $f$ is a function which belongs to a Hardy field and which satisfies $|f(x)|\\prec x^{\\ell}$ for some $\\ell\\in \\mathbb{N}$, then the sequence $(f(n))_{n\\in \\mathbb{N}}$ is uniformly distributed modulo 1 if and only if $\\lim_{x\\to\\infty}\\frac{|f(x)-p(x)|}{\\log(x)} = \\infty$ for all $p(x)\\in \\mathbb{Q}[x]$. We provide a new proof of this result using methods from summability theory and we extend Boshernitzan's criterion by obtaining necessary and sufficient conditions for $f$ to be uniformly distributed modulo 1 with respect to a broad class of w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08040","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/2606.08040/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"}