Counting Singular Matrices with Primitive Row Vectors
| dc.creator | Wigman, Igor | |
| dc.date | 2003-05-04 | |
| dc.date | 2003-11-30 | |
| dc.date.accessioned | 2026-07-07T04:57:45Z | |
| dc.date.available | 2026-07-07T04:57:45Z | |
| dc.description | We solve an asymptotic problem in the geometry of numbers, where we count the number of singular $n\times n$ 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 \to \infty $, the number is asymptotic to $ \frac{(n-1)u_n}{ζ(n) ζ(n-1)^{n}}T^{n^{2}-n}\log (T)$ for $n \ge 3$. The 3-dimensional case is the most problematic and we need to invoke an equidistribution theorem due to W. Schmidt. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0305066 | |
| dc.identifier | http://arxiv.org/abs/math/0305066 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67368 | |
| dc.subject | Number Theory | |
| dc.title | Counting Singular Matrices with Primitive Row Vectors | |
| dc.type | text |