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arXiv · 1909.04581

Explicit Salem sets in $\mathbb{R}^n$

Robert Fraser·Kyle Hambrook
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Abstract

We construct the first explicit (i.e., non-random) examples of Salem sets in $\mathbb{R}^n$ of arbitrary prescribed Hausdorff dimension. This completely resolves a problem proposed by Kahane more than 60 years ago. The construction is based on a form of Diophantine approximation in number fields.

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Robert Fraser, Kyle Hambrook. 2019-09-10. Explicit Salem sets in $\mathbb{R}^n$. https://arxiv.org/abs/1909.04581

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