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arXiv · 2610.34973

Counting Integral Matrices with Given Cubic Characteristic Polynomial

Philipp Habegger
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Abstract

We show that the number of $3\times 3$ matrices with given characteristic polynomial and entries in $\mathbb{Z}\cap [-H,H]$ is at most $c H^{3}(\log H)^{6}$ for all $H\ge 2$, where $c>0$ is an absolute constant.

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Philipp Habegger. 2026-10-26. Counting Integral Matrices with Given Cubic Characteristic Polynomial. https://arxiv.org/abs/2610.34973

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