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

El-Baz, Daniel

doi:10.4064/aa181121-26-3

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

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El-Baz, Daniel
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.4064/aa181121-26-3
(Publisher version)

https://doi.org/10.48550/arXiv.1811.01919
(Preprint)

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Citation

El-Baz, D. (2020). An analogue of the Erdős-Kac theorem for the special linear group over the integers. Acta Arithmetica, 192(2), 181-188. doi:10.4064/aa181121-26-3.

Cite as: https://hdl.handle.net/21.11116/0000-0006-D8AE-3

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 Erd\H{o}s-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.