A solution to a problem of Cassels and Diophantine properties of cubic numbers
A solution to a problem of Cassels and Diophantine properties of cubic numbers
We prove that almost any pair of real numbers α, β, satisfies the following inhomogeneous uniform version of Littlewood's conjecture:where • denotes the distance from the nearest integer.The existence of even a single pair that satisfies statement (C1), solves a problem of Cassels from the 50's.We then prove that if …