{"title":"Sharp Fourier decay estimates for measures supported on the well-approximable numbers","authors":"Robert Fraser, Thanh Nguyen","doi":"arxiv-2409.02854","DOIUrl":null,"url":null,"abstract":"We construct a measure on the well-approximable numbers whose Fourier\ntransform decays at a nearly optimal rate. This gives a logarithmic improvement\non a previous construction of Kaufman.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"36 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Classical Analysis and ODEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.02854","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We construct a measure on the well-approximable numbers whose Fourier
transform decays at a nearly optimal rate. This gives a logarithmic improvement
on a previous construction of Kaufman.
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