Geometry, Topology and Dynamics Seminar
Uri Shapira
Hebrew University, Jerusalem
A solution to an open problem of Cassels and Diophantine properties of cubic numbers
Abstract: We prove existence of real numbers x,y, possessing the following property:
For any real $a,b$, $liminf |n| \|nx - a\| \|ny - b\| = 0$,
where $\|c\|$ denotes the distance of $c$ to the nearest integer.
This answers a 50 years old question of Cassels.
The most interesting part of the result is that there are algebraic
numbers with the above property!
Monday February 16, 2009 at 3:00 PM in SEO 612