English

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

Classical Analysis and ODEs 2021-05-25 v1

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 Zpq×ZpqZp2×Zq2\mathbb{Z}_{pq} \times \mathbb{Z}_{pq} \cong \mathbb{Z}_p^2 \times \mathbb{Z}_q^2.

Keywords

Cite

@article{arxiv.2105.10575,
  title  = {Spectral sets and tiles in $\mathbb{Z}_p^2 \times \mathbb{Z}_q^2$},
  author = {Thomas Fallon and Gergely Kiss and Gábor Somlai},
  journal= {arXiv preprint arXiv:2105.10575},
  year   = {2021}
}

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15 pages