We show that if A is a set of mutually orthogonal exponentials with respect to the unit disk then |A ∩ [-R, R]²| _ε R3/5+ε holds. This improves the previous bound of R2/3 by Iosevich--Kolountzakis. The main new ingredient in the proof is a variant of Marstrand's projection theorem.
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Dmitrii Zakharov (2024) studied this question.
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