Projects per year
Abstract
The Littlewood Conjecture states that liminf_{q\to \infty} q . ||qx|| . ||qy|| = 0 for all pairs (x,y) of real numbers. We show that with the additional factor of log q . loglog q the statement is false. Indeed, our main result implies that the set of (x,y) for which liminf_{q\to\infty} q . log q . loglog q . ||qx|| . ||qy|| > 0 is of full dimension.
Original language | English |
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Number of pages | 22 |
Publication status | Published - Jan 2011 |
Projects
- 1 Finished
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Inhomogenous approximation on manifolds
15/02/08 → 14/04/11
Project: Research project (funded) › Research