Fuglede's conjecture holds on ℤ_p² × ℤ_q

2019/12/15 by Gergely Kiss, Kiss, Gergely, Gábor Somlai +1
Mathematics · #Advanced Algebra and Geometry #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1912.07114

openalex publication_date 2019/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The study of Fuglede's conjecture on the direct product of elementary abelian groups was initiated by Iosevich et al. For the product of two elementary abelian groups the conjecture holds. For ℤ_p³ the problem is still open if p≥ 11. In connection we prove that Fuglede's conjecture holds on ℤ_p²× ℤ_q by developing a method based on ideas from discrete geometry.

Citations

• Complex Hadamard matrices and the Spectral Set Conjecture
• Tiles with no spectra
• Spectrum is rational in dimension one

Related

• Spectral sets and tiles in ℤ_p² × ℤ_q²
• Fuglede's conjecture holds in ℤ_p×ℤ_pⁿ
• A linear programming approach to Fuglede's conjecture in ℤ_p³
• Spectral Tile Direction in the Group ℤ_p² × ℤ_q² × ℤ_r
• The Fuglede conjecture holds in ℤ³₅