For an arbitrarily given irreducible polynomial χ(x) in Z{x} of degree n, let N (X, T ) be the number of n × n matrices over Z whose characteristic polynomial is χ(x), bounded by a positive number T with respect to a certain norm. We provide an asymptotic formula for N (X, T ) as T → ∞ in terms of the orbital integrals of gln. This generalizes the work of A. Eskin, S. Mozes, and N. Shah (1996) which assumed that Z{x}/(χ(x)) is the ring of integers. In addition, we will provide an asymptotic formula for N (X, T ), using the orbital integrals of gln, when Q is generalized to a totally real number field k and when n is a prime number. Here we need a mild restriction on splitness of χ(x) over kv at p-adic places v of k for p ≤ n when k[x]/(χ(x)) is unramified Galois over k. This is a joint work with Seoungsu Jeon.