Sharp Fourier decay estimates for measures supported on the well-approximable numbers

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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Publication Details

Journal
Annales Fennici Mathematici
Published
2025-08-25
DOI
https://doi.org/10.54330/afm.163951
Primary Topic
Advanced Mathematical Physics Problems
Type
article
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article

Sharp Fourier decay estimates for measures supported on the well-approximable numbers

Robert Fraser, Thanh Nguyen
Annales Fennici Mathematici
Advanced Mathematical Physics Problems
article

Sharp Fourier decay estimates for measures supported on the well-approximable numbers

Robert Fraser, Thanh Nguyen
article en

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.

Annales Fennici MathematiciVol. 50(2)
Wichita State University (US), Indiana University (US)
Openalex Percentile: Top 72%
Advanced Mathematical Physics Problems
DOIOpen Access PDFOpenAlex
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Sharp Fourier decay estimates for measures supported on the well-approximable numbers — Robert Fraser, Thanh Nguyen · Annales Fennici Mathematici (2025) | TGRS Research Map | TGRS