The Fuglede Conjecture holds in \(\F_p^3\) for p=5,7

Abstract

For p=5,7, we show that a subset \(E \subset \F_p^3\) is spectral if and only if E tiles \(\F_p^3\) by translation. Additionally, we give an alternate proof that the conjecture holds for p=3.

The results were originally announced in May 2018 in a frame workshop at ICERM