The Fuglede Conjecture holds in ${\mathbb{Z}}_p\times {\mathbb{Z}}_p$

Alex Iosevich, Azita Mayeli, Jonathan Pakianathan

In this paper we study subsets $E$ of ${\mathbb{Z}}_p^d$ such that any function $f:E\to \mathbb{C}$ can be written as a linear combination of characters orthogonal with respect to $E$.…