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

Authors

  • Robert Fraser Wichita State University, Mathematics and Statistics
  • Thanh Nguyen Indiana University, Department of Mathematics

DOI:

https://doi.org/10.54330/afm.163951

Keywords:

Harmonic analysis, geometric measure theory, Diophantine approximation, Hausdorff dimension

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.

Downloads

Published

2025-08-25

Issue

Vol. 50 No. 2 (2025)

Section

Articles

License

Copyright (c) 2025 Annales Fennici Mathematici

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Sharp Fourier decay estimates for measures supported on the well-approximable numbers. (2025). Annales Fennici Mathematici, 50(2), 483–510. https://doi.org/10.54330/afm.163951