# A randomized version of the Littlewood Conjecture – Part I – Henna Koivusalo (University of Vienna)

#### Venue

Sala Conferenze (Puteano, Centro De Giorgi).

#### Abstract

The Littlewood Conjecture in Diophantine approximation can be thought of as a problem about covering the plane by a union of hyperbolas centered at rational points. In this paper we consider the problem of translating the center of each hyperbola by a random amount which depends on the denominator of the corresponding rational. Using a randomized covering argument we prove that, not only is this randomized version of the Littlewood Conjecture true for almost all choices of centers, but an even stronger statement with an extra factor of a logarithm also holds. This work is joint with Alan Haynes (Houston).

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