Fourier Dimension Estimates for Sets of Exact Approximation Order: The Badly-Approximable Case

Robert Fraser, Reuben Wheeler

We show for decreasing, positive approximation functions $\psi$ such that $\tau ={\lim }_{q\to \infty }\frac{\log \psi (q)}{\log q}<\frac{13+\sqrt{73}}{8}$ and such that $q^2\psi (q)\to 0$ t…