Fuglede’s conjecture holds on ℤ_{𝕡}²×ℤ_{𝕢}

Author:

Kiss Gergely,Somlai Gábor

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 p 3 \mathbb {Z}_p^3 the problem is still open if p p is prime and p 11 p\ge 11 . In connection we prove that Fuglede’s conjecture holds on Z p 2 × Z q \mathbb {Z}_{p}^2\times \mathbb {Z}_q by developing a method based on ideas from discrete geometry.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

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