Uri Shapira (Hebrew University)
A solution to an open problem of Cassels and Diophantine
properties of cubic numbers.
The abstract is:
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!