{"paper":{"title":"Averaged Fourier Estimates and Dyadic Approximation on the Cantor set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Prasuna Bandi","submitted_at":"2026-06-25T13:40:41Z","abstract_excerpt":"Let $C$ be the middle-third Cantor set and let $\\mu$ be the natural Cantor probability measure. Let \\[ \\gamma=\\frac{\\log2}{\\log3}. \\] The two main results of this paper are \\[ \\mu\\{x\\in C:\\|2^n x\\|<n^{-\\tau}\\text{ for infinitely many }n\\}=0 \\qquad \\text{ for } \\tau>2-\\gamma. \\] and \\[ \\mu\\{x\\in C:\\|2^n x\\|<n^{-\\tau}\\text{ for infinitely many }n\\}=1 \\qquad \\text{ for } \\tau<\\frac{1-\\gamma}{2}. \\] These results give new progress toward Velani's conjecture on zero-one law for dyadic approximation in the middle-third Cantor set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27034","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/2606.27034/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"}