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arXiv · 2502.07100

Counting matrices over finite rank multiplicative groups

Aaron Manning·Alina Ostafe·Igor E. Shparlinski
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Abstract

Motivated by recent works on statistics of matrices over sets of number theoretic interest, we study matrices with entries from arbitrary finite subsets $\mathcal A$ of finite rank multiplicative groups infields of characteristic zero. We obtain upper bounds, in terms of the size of $\mathcal A$, on the number of such matrices of a given rank, with a given determinant and with a prescribed characteristic polynomial. In particular, in the case of ranks, our results can be viewed as a statistical version of work by Alon and Solymosi (2003).

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Aaron Manning, Alina Ostafe, Igor E. Shparlinski. 2025-02-10. Counting matrices over finite rank multiplicative groups. https://doi.org/10.2140/pjm.2026.340.115

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