Year: 2025
Type: preprint
Abstract: We consider the set ${\mathcal M}_n\left({\mathbb Z}; H\right)$ of $n\times n$-matrices with integer elements of size at most $H$ and obtain an asymptotic formula for the number of matrices from ${\mathcal M}_n\left({\mathbb Z}; H\right)$ with square-free determinants. We also use our approach with some further enhancements to obtain an asymptotic formula for the sums of the Euler function with determinants of matrices from ${\mathcal M}_n\left({\mathbb Z}; H\right)$.
Source: arXiv (Cornell University)
Authors: Ostafe, Alina, Shparlinski, Igor E.
Institution: UNSW Sydney
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979329759
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