Note on Robins' Conjecture in Dimension Four and Higher

Fuente: arXiv
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Main Author: Asipchuk, Oleg
Format: Preprint
Published: 2025
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author Asipchuk, Oleg
author_facet Asipchuk, Oleg
contents This article is motivated by a conjecture proposed by Sinai Robins in 2024. The conjecture asserts that two convex, centrally symmetric sets of positive measure that are not multi-tilers must coincide up to rigid motions if and only if their Fourier transforms agree on the lattice $\mathbb{Z}^d$. In this paper, we disprove the conjecture by constructing explicit counterexamples in dimensions $d \geq 4$.
format Preprint
id arxiv_https___arxiv_org_abs_2509_26587
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Note on Robins' Conjecture in Dimension Four and Higher
Asipchuk, Oleg
Functional Analysis
42C15, 42C30
This article is motivated by a conjecture proposed by Sinai Robins in 2024. The conjecture asserts that two convex, centrally symmetric sets of positive measure that are not multi-tilers must coincide up to rigid motions if and only if their Fourier transforms agree on the lattice $\mathbb{Z}^d$. In this paper, we disprove the conjecture by constructing explicit counterexamples in dimensions $d \geq 4$.
title Note on Robins' Conjecture in Dimension Four and Higher
topic Functional Analysis
42C15, 42C30
url https://arxiv.org/abs/2509.26587