Consider $G=GL(n,q)$. A regular semisimple element of this group, is a matrix, whose characterestic polynomial is square-free and same as minimal polynomial. Results show that the number of such matrices in $G$ is a polynomial in $q$, with degree $n^2$, and coefficient of the leading term being 1.
Does similar hold, when we take $G=SL(n,q)$, that is, the number of such matrices in $G$ is given by a polynomial in $q$ of degree $n^2-1$, with the leading term being 1?
I appreciate any kind of help or references that can be of use. Thank you.