Counting nonsingular matrices with primitive row vectors

Abstract

We give an asymptotic expression for the number of nonsingular integer n-by-n-matrices with primitive row vectors, determinant k, and Euclidean matrix norm less than T, for large T. We also investigate the density of matrices with primitive rows in the space of matrices with determinant k, and determine its asymptotics for large k.

arXiv comment21 pages. Fixed proof of monotonicity of the density function. Added a result on the image of the density function