Littlewood’s conjecture

We classify the measures on SL(k, R)/ SL(k, Z) which are invariant and ergodic under the action of the group A of positive diagonal matrices with positive entropy. We apply this to prove that the set of exceptions to Littlewood’s conjecture has Hausdorff dimension zero. 1. Introduction 1.1. Number theory and dynamics. There is a long and rich tradition of applying dynamical methods to number theory.

49p noel_noel 17-01-2013 47 8   Download