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A counterexample to Fuglede’s conjecture in (Z/pZ) 4 for all odd primes

Journal Contribution - Journal Article

We construct a spectral, non-tiling set of size 2p in (Z/pZ)4, p odd prime. This example complements a previous counterexample in [C. Aten et al., Tiling sets and spectral sets over finite fields, arXiv:1509.01090], which existed only for p ≡ 3 (mod 4). On the contrary we show that the conjecture does hold in (Z/2Z)4.

Journal: Bulletin of the Belgian Mathematical Society Simon Stevin
ISSN: 1370-1444
Issue: 4
Volume: 27
Pages: 481-488
Number of pages: 8
Publication year:2020
Keywords:Pure mathematics