Counting nonsingular matrices with primitive row vectors
Number Theory
2013-09-03 v2
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.
Cite
@article{arxiv.1211.2716,
title = {Counting nonsingular matrices with primitive row vectors},
author = {Samuel Holmin},
journal= {arXiv preprint arXiv:1211.2716},
year = {2013}
}
Comments
21 pages. Fixed proof of monotonicity of the density function. Added a result on the image of the density function