Spectral sets and tiles in ℤ_p² × ℤ_q²

2021/05/21 by Thomas Fallon, Fallon, Thomas, Gergely Kiss +3
Mathematics · #05B25 #20K01 #43A65 (Primary) #52C20 (Secondary) #Advanced Algebra and Geometry #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2105.10575

openalex publication_date 2021/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ℤ_pq × ℤ_pq ≅ ℤ_p² × ℤ_q².

Citations

• Complex Hadamard matrices and the Spectral Set Conjecture
• Tiles with no spectra

Related

• Spectral Tile Direction in the Group ℤ_p² × ℤ_q² × ℤ_r
• Spectral sets in ℤ_p²qr tile
• Fuglede's conjecture holds on ℤ_p² × ℤ_q
• A group ring approach to Fuglede's conjecture in cyclic groups
• Fuglede's conjecture holds in ℚ_p