Counting Singular Matrices with Primitive Row Vectors |
| |
Authors: | Igor Wigman |
| |
Institution: | (1) Tel Aviv University, Israel |
| |
Abstract: | We solve an asymptotic problem in the geometry of numbers, where we count the number of singular n×n matrices where row vectors are primitive and of length at most T. Without the constraint of primitivity, the problem was solved by Y. Katznelson. We show that as T, the number is asymptotic to
for n3. The 3-dimensional case is the most problematic and we need to invoke an equidistribution theorem due to W. M. Schmidt. |
| |
Keywords: | 2000 Mathematics Subject Classification: 11H06 |
本文献已被 SpringerLink 等数据库收录! |