An asymptotic formula for the number of integral matrices with a fixed characteristic polynomial via orbital integrals

Seongsu Jeon, Yuchan Lee

For an irreducible polynomial $\chi (x)\in {\mathcal{O}}_k[x]$ of degree $n$, where $k$ is a number field and ${\mathcal{O}}_k$ its ring of integers, let $N(X,T)$ denote the number of $n…