On sets of orthogonal exponentials on the disk

We show that if $A$ is a set of mutually orthogonal exponentials with respect to the unit disk then $|A \cap [-R, R]^2| \lesssim_\varepsilon R^{3/5+\varepsilon}$ holds. This improves the previous bound of $R^{2/3}$ by Iosevich--Kolountzakis. The main new ingredient in the proof is a discretized version of Marstrand's slicing theorem.