Projects per year
Abstract
We solve the problem of giving sharp asymptotic bounds on the Hausdorff dimensions of certain sets of badly approximable matrices, thus improving results of Broderick and Kleinbock (preprint 2013) as well as Weil (preprint 2013), and generalizing to higher dimensions those of Kurzweil ('51) and Hensley ('92). In addition we use our technique to compute the Hausdorff $f$measure of the set of matrices which are not $\psi$approximable, given a dimension function $f$ and a function $\psi:(0,\infty)\to (0,\infty)$. This complements earlier work by Dickinson and Velani ('97) who found the Hausdorff $f$measure of the set of matrices which are $\psi$approximable.
Original language  English 

Pages (fromto)  413459 
Number of pages  47 
Journal  Mathematical Proceedings of the Cambridge Philosophical Society 
Volume  164 
Issue number  3 
Early online date  5 Apr 2017 
DOIs  
Publication status  Published  May 2018 
Bibliographical note
© Cambridge Philosophical Society 2017. This is an authorproduced version of the published paper. Uploaded in accordance with the publisher’s selfarchiving policy. Further copying may not be permitted; contact the publisher for detailsKeywords
 math.NT
Projects
 1 Finished

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