The Fuglede conjecture holds in $\mathbb{Z}^3_5$
Classical Analysis and ODEs
2019-02-07 v1 Combinatorics
Number Theory
Abstract
The Fuglede conjecture states that a set is spectral if and only if it tiles by translation. The conjecture was disproved by T. Tao for dimensions 5 and higher by giving a counterexample in . We present a computer program that determines that the Fuglede conjecture holds in by exhausting the search space. A. Iosevich, A. Mayeli and J. Pakianathan showed that the Fuglede conjecture holds over prime fields when the dimension does not exceed 2. The question for dimension 3 was previously addressed by Aten et al. for . In this paper we build upon the results of their work to allow a computer to carry out the lengthy computations.
Keywords
Cite
@article{arxiv.1902.01916,
title = {The Fuglede conjecture holds in $\mathbb{Z}^3_5$},
author = {Philipp Birklbauer},
journal= {arXiv preprint arXiv:1902.01916},
year = {2019}
}