2024/09/03 by T. D. Browning, Will Sawin, Browning, Tim +3
Engineering · Mathematics · Computer Science · #graph theory and CDMA systems #Advanced Optimization Algorithms Research #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2409.01920
We prove upper and lower bounds on the number of pairs of commuting n× n matrices with integer entries in [-T,T], as T→ ∞. Our work uses Fourier analysis and leads us to an analysis of exponential sums involving matrices over finite fields. These are bounded by combining a stratification result of Fouvry and Katz with a new result about the flatness of the commutator Lie bracket.