An analogue of the Erdős-Kac theorem for the special linear group over the integers

2018/11/05 by Daniel El-Baz, El-Baz, Daniel
Engineering · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1811.01919

openalex publication_date 2018/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the number of prime factors of individual entries for matrices in the special linear group over the integers. We show that, when properly normalised, it satisfies a central limit theorem of Erdős-Kac-type. To do so, we employ a sieve-theoretic set-up due to Granville and Soundararajan. We also make use of an estimate coming from homogeneous dynamics due to Gorodnik and Nevo.

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