Counting nonsingular matrices with primitive row vectors
  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. 
Samuel Holmin
math.NT