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math.DS2008★ 2 cited
On a generalization of Littlewood's conjecture
Uri Shapira
We present a class of lattices in R^d (d >= 2) which we call GL-lattices and conjecture that any lattice is such. This conjecture is referred to as GLC. Littlewood's conjecture amo…
math.DS2008★ 4 cited
A solution to a problem of Cassels and Diophantine properties of cubic numbers
Uri Shapira
We prove that almost any pair of real numbers a,b, satisfies the following inhomogeneous uniform version of Littlewood's conjecture: (*) forall x,y in R, liminf_{|n|\to\infty} |n|<…