On the Exact Fourier Dimension of Sets of Well-Approximable Matrices

2024/03/28 by Thomas Cai, Cai, Thomas, Kyle Hambrook +1
Computer Science · Mathematics · #Approximation Theory and Sequence Spaces #Digital Image Processing Techniques #FOS: Mathematics #Matrix Theory and Algorithms #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2403.19410

openalex publication_date 2024/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the exact Fourier dimension of the set of Ψ-well-approximable m × n matrices (and the set of Ψ-well-approximable numbers) in the homogeneous and inhomogeneous cases for any approximation function Ψ satisfying ∑_{q ∈ ℤⁿ} Ψ(q)^m < ∞.

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