Projects per year
Abstract
In this article, we develop the convergence theory of simultaneous, inhomogeneous Diophantine approximation on manifolds. A consequence of our main result is that if the manifold M ⊂ ℝ ^{n} is of dimension strictly greater than (n+1)/2 and satisfies a natural nondegeneracy condition, then M is of Khintchine type for convergence. The key lies in obtaining essentially the best possible upper bound regarding the distribution of rational points near manifolds.
Original language  English 

Pages (fromto)  28852908 
Number of pages  24 
Journal  International Mathematics Research Notices 
Volume  2017 
Issue number  10 
Early online date  14 Jun 2016 
DOIs  
Publication status  Published  1 May 2017 
Bibliographical note
© 2016, The Author(s).Profiles
Projects
 2 Finished

Diophantine properties of Mahler´s numbers
1/07/15 → 30/06/17
Project: Research project (funded) › Research

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