Some Effective Estimates in Reduction Theory of Quadratic Forms
Presenter
May 14, 2015
Keywords:
- bilinear forms
- bilinear forms over integers
- SL(3,Z)
- Hermite-Minkowski theorem
- indefinite forms
MSC:
- 37-XX
- 37AXX
- 37A20
- 11D09
- 22Exx
- 14Qxx
- 14Q20
Abstract
The aim of this talk is to present a recent joint work with Professor Gregory A. Margulis. Our main result is that any indefinite ternary integral quadratic form is integrally equivalent to many forms whose coefficients are small. This is deduced from a concentration property of the periodic SO(1, 2)-orbits in SL(3, R)/SL(3,Z).