Spectral sets and tiles in ${\mathbb{Z}}_p^2\times {\mathbb{Z}}_q^2$

Abstract

In this paper we study Fuglede's conjecture on the direct product of two cyclic groups. After collecting the known results we prove that Fuglede's conjecture holds on ${\mathbb{Z}}_{pq}\times {\mathbb{Z}}_{pq}\cong {\mathbb{Z}}_p^2\times {\mathbb{Z}}_q^2$.

arXiv comment15 pages

References in corpus (4)

• Complex Hadamard matrices and the Spectral Set Conjecture
• Fuglede's conjecture fails in 4 dimensions over odd prime fields
• On the structure of spectral and tiling subsets of cyclic groups
• Addendum to "Fuglede's conjecture fails in 4 dimensions over odd prime fields"