Projects per year
Abstract
For any i,j≥0 with i+j=1 , let Bad(i,j) denote the set of points (x,y)∈R 2 for which max{∥qx∥ 1/i ,∥qy∥ 1/j }>c/q for all q∈N . Here c=c(x,y) is a positive constant. Our main result implies that any finite intersection of such sets has full dimension. This settles a conjecture of Wolfgang M. Schmidt in the theory of simultaneous Diophantine approximation.
Original language  English 

Pages (fromto)  18371883 
Number of pages  46 
Journal  Annals of Mathematics 
Volume  174 
Issue number  3 
DOIs  
Publication status  Published  Nov 2011 
Keywords
 Number Theory
Projects
 2 Finished

Classical metric Diophantine approximation revisited
24/03/08 → 23/07/11
Project: Research project (funded) › Research

Inhomogenous approximation on manifolds
15/02/08 → 14/04/11
Project: Research project (funded) › Research