A randomized version of the Littlewood Conjecture

Research output: Working paper


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, an even stronger statement with an extra factor of a logarithm also holds.
Original languageUndefined/Unknown
Publication statusPublished - 25 Oct 2016

Bibliographical note

6 pages, newer version: added reference [1]


  • math.NT
  • 11J13, 60D05

Cite this