Projects per year
Abstract
Let C be two times continuously differentiable curve in R^2 with at least one point at which the curvature is nonzero. For any i,j > 0 with i+j =1, let Bad(i,j) denote the set of points (x,y) in R^2 for which max {qx ^{1/i}, qy^{1/j}} > c/q for all integers q >0. Here c = c(x,y) is a positive constant. Our main result implies that any finite intersection of such sets with C has full Hausdorff dimension. This provides a solution to a problem of Davenport dating back to the sixties.
Original language  English 

Pages (fromto)  9691023 
Number of pages  55 
Journal  Mathematische Annalen 
Volume  359 
Issue number  34 
Early online date  1 Mar 2014 
DOIs  
Publication status  Published  Aug 2014 
Bibliographical note
44 pagesKeywords
 math.NT
 11J83, 11J13, 11K60
Profiles
Projects
 3 Finished

Programme GrantNew Frameworks in metric Number Theory
1/06/12 → 30/11/18
Project: Research project (funded) › Research

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