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

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.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0006-D8AE-3 Version Permalink: https://hdl.handle.net/21.11116/0000-000D-EC57-8
Genre: Journal Article
Latex : An analogue of the Erd\H{o}s-Kac theorem for the special linear group over the integers

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arXiv:1811.01919.pdf (Preprint), 156KB
 
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https://doi.org/10.4064/aa181121-26-3 (Publisher version)
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 Creators:
El-Baz, Daniel1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Number Theory, Dynamical Systems
 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.

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Language(s): eng - English
 Dates: 2020
 Publication Status: Issued
 Pages: 8
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1811.01919
DOI: 10.4064/aa181121-26-3
 Degree: -

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Project name : -
Grant ID : 320755
Funding program : Funding Programme 7 (FP7)
Funding organization : European Commission (EC)

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Title: Acta Arithmetica
  Abbreviation : Acta Arith.
Source Genre: Journal
 Creator(s):
Affiliations:
Publ. Info: Institute of Mathematics, Polish Academy of Sciences
Pages: - Volume / Issue: 192 (2) Sequence Number: - Start / End Page: 181 - 188 Identifier: -