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arXiv · 2503.13768

Counting integer matrices with square-free determinants

Alina Ostafe·Igor E. Shparlinski
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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 and asymptotic formula on 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 $\mathcal M_n\left(\mathbb Z; H\right)$.

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Alina Ostafe, Igor E. Shparlinski. 2025-03-17. Counting integer matrices with square-free determinants. https://arxiv.org/abs/2503.13768

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