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arXiv · 2408.04350

On the determinants of matrices with elements from arbitrary sets

Ilya D. Shkredov·Igor E. Shparlinski
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Abstract

Recently there has been several works estimating the number of $n\times n$ matrices with elements from some finite sets $\mathcal X$ of arithmetic interest and of a given determinant. Typically such results are compared with the trivial upper bound $O(X^{n^2-1})$, where $X$ is the cardinality of $\mathcal X$. Here we show that even for arbitrary sets $\mathcal X\subseteq \mathbb R$,some recent results from additive combinatorics enable us to obtain a stronger bound with a power saving.

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Ilya D. Shkredov, Igor E. Shparlinski. 2024-08-08. On the determinants of matrices with elements from arbitrary sets. https://arxiv.org/abs/2408.04350

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