Diophantine approximation for algebraic numbers
Presenter
May 12, 2015
Keywords:
- well-approximable numbers
- Diophantine approximation
- Liouville number
- transcendental number theory
- homogeneous dynamics orbit
- Raghunathan's theorem
MSC:
- 11-xx
- 11Jxx
- 11J04
- 11J68
- 11J68
- 11J99
- 11Kxx
- 11K16
- 11K60
- 37-xx
- 37A20
Abstract
A number is well approximable (WA) if the error when approximatin by p/q can be made small compared to the sqare of 1/q. Almost all reals are WA. For good reasons quadratic irrationals are not. Nothing is known for cubic irrationals. We show how this relates to special orbits in homogeneous dynamics.