Metrical musings on Littlewood and friends

Abstract:

The celebrated Littlewood conjecture in Diophantine approximation concerns the simultaneous approximation of two real numbers by rationals with the same denominator. A cousin of this conjecture is the mixed Littlewood conjecture of de Mathan and Teulié, which is concerned with the approximation of a single real number, but where some denominators are preferred to others.

In the talk, we will derive a metrical result extending work of Pollington and Velani on the Littlewood conjecture.

Our result implies the existence of an abundance of numbers satisfying both conjectures.

This is joint work with Alan Haynes and Jonas Lindstrøm Jensen.