Counting Integral Matrices with Given Cubic Characteristic Polynomial

Philipp Habegger

Source record

Source: arXiv

Published: Oct 26, 2026

arXiv: 2610.34973

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Source 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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Counting Integral Matrices with Given Cubic Characteristic Polynomial — Mathematical Frontier Network