Spectral sets in $\mathbb{Z}_{p^2qr}$ tile
Classical Analysis and ODEs
2023-05-26 v3
Authors:
Gábor Somlai
Abstract
We prove the every spectral set in Zp2qr tiles, where p, q and r are primes. Combining this with a recent result of Malikiosis we obtain that Fuglede's conjecture holds for Zp2qr.
Cite
@article{arxiv.1907.04398,
title = {Spectral sets in $\mathbb{Z}_{p^2qr}$ tile},
author = {Gábor Somlai},
journal= {arXiv preprint arXiv:1907.04398},
year = {2023}
}
Related papers
View all related →
Classical Analysis and ODEs · Mathematics
Fuglede's conjecture holds on cyclic groups $\mathbb{Z}_{pqr}$
Ruxi Shi
2019-10-15
Classical Analysis and ODEs · Mathematics
Spectral sets and tiles in $\mathbb{Z}_p^2 \times \mathbb{Z}_q^2$
Thomas Fallon, Gergely Kiss, Gábor Somlai
2021-05-25
Classical Analysis and ODEs · Mathematics
Tiling sets and spectral sets over finite fields
C. Aten, B. Ayachi, E. Bau, D. FitzPatrick +13
2015-09-04
Functional Analysis · Mathematics
Some reductions of the spectral set conjecture to integers
Dorin Ervin Dutkay, Chun-Kit Lai
2014-01-14
Classical Analysis and ODEs · Mathematics
Spectrality of Prime Size Tiles
Weiqi Zhou
2026-03-10
Classical Analysis and ODEs · Mathematics
Spectral Tile Direction in the Group $\mathbb{Z}_{p^2} \times \mathbb{Z}_{q^2} \times \mathbb{Z}_r$
Thomas Fallon, Gergely Kiss, Azita Mayeli, Gábor Somlai
2024-12-03
Classical Analysis and ODEs · Mathematics
Equi-distributed property and spectral set conjecture on $\mathbb{Z}_{p^2}\times \mathbb{Z}_{p}$
Ruxi Shi
2020-05-27
Classical Analysis and ODEs · Mathematics
The Fuglede Conjecture holds in ${\Bbb Z}_p \times {\Bbb Z}_p$
Alex Iosevich, Azita Mayeli, Jonathan Pakianathan
2017-06-14
Classical Analysis and ODEs · Mathematics
Fuglede's conjecture on cyclic groups of order $p^n q$
Romanos-Diogenes Malikiosis, Mihail N. Kolountzakis
2020-05-04
Combinatorics · Mathematics
A group ring approach to Fuglede's conjecture in cyclic groups
Tao Zhang
2022-11-01
Classical Analysis and ODEs · Mathematics
The Fuglede conjecture holds in $\mathbb{Z}^3_5$
Philipp Birklbauer
2019-02-07
Classical Analysis and ODEs · Mathematics
Fuglede's conjecture holds in $\mathbb{Q}_p$
Aihua Fan, Shilei Fan, Lingmin Liao, Ruxi Shi
2015-12-31
Number Theory · Mathematics
Spectra of certain types of polynomials and tiling of integers with translates of finite sets
Sergei Konyagin, Izabella Laba
2007-05-23
Number Theory · Mathematics
Fuglede's conjecture fails in 4 dimensions over odd prime fields
Samuel Ferguson, Nat Sothanaphan
2020-11-10
Classical Analysis and ODEs · Mathematics
On Tiling and Spectral Sets in $\mathbb Z_{p^2}\times\mathbb Z_{p^2}$
Weiqi Zhou
2026-03-24
Classical Analysis and ODEs · Mathematics
Tiling the field $\mathbb{Q}_p$ of $p$-adic numbers by a function
Shilei Fan
2025-01-15
Classical Analysis and ODEs · Mathematics
On the discrete Fuglede and Pompeiu problems
Gergely Kiss, Romanos Diogenes Malikiosis, Gábor Somlai, Máté Vizer
2020-05-04
Functional Analysis · Mathematics
Spectrality of Self-Similar Tiles
Xiaoye Fu, Xinggang He, Ka-Sing Lau
2013-09-17
Classical Analysis and ODEs · Mathematics
Fuglede's spectral set conjecture for convex polytopes
Rachel Greenfeld, Nir Lev
2018-03-16
Classical Analysis and ODEs · Mathematics
Spectral sets and weak tiling
Mihail N. Kolountzakis, Nir Lev, Máté Matolcsi
2023-10-24
Classical Analysis and ODEs · Mathematics
Fuglede's conjecture for a union of two intervals
I. Laba
2007-05-23
Classical Analysis and ODEs · Mathematics
Fuglede's conjecture holds for cyclic groups of order $pqrs$
Gergely Kiss, Romanos Diogenes Malikiosis, Gábor Somlai, Máté Vizer
2023-01-05
Classical Analysis and ODEs · Mathematics
The Fuglede Conjecture holds in \(\F_p^3\) for p=5,7
Thomas Fallon, Azita Mayeli, Dominick Villano
2019-06-11
Functional Analysis · Mathematics
Some Plancherel identities for unbounded subsets of $\mathbb R$ in duality
Piyali Chakraborty, Dorin Ervin Dutkay
2026-03-05
Classical Analysis and ODEs · Mathematics
Spectrality of product domains and Fuglede's conjecture for convex polytopes
Rachel Greenfeld, Nir Lev
2018-07-03