Projects per year
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, an even stronger statement with an extra factor of a logarithm also holds.
Original language  Undefined/Unknown 

Publication status  Published  25 Oct 2016 
Bibliographical note
6 pages, newer version: added reference [1]Keywords
 math.NT
 11J13, 60D05
Projects
 3 Finished

Gaps theorems and statistics of patterns in quasicrystals
1/07/15 → 30/06/18
Project: Research project (funded) › Research

Diophantine approximation, chromatic number, and equivalence classes of separated nets
10/10/13 → 9/07/15
Project: Research project (funded) › Research

Career Acceleration Fellowship: Circle rotations and their generalisation in Diophantine approximation
1/10/13 → 30/09/16
Project: Research project (funded) › Research