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arXiv · 1811.01919

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

Daniel El-Baz
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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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Daniel El-Baz. 2019-11-01. An analogue of the Erdős-Kac theorem for the special linear group over the integers. https://arxiv.org/abs/1811.01919

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