Projects per year
Abstract
For any j_1,...,j_n>0 with j_1+...+j_n=1 and any x \in R^n, we consider the
set of points y \in R^n for which max_{1\leq i\leq n}(qx_iy_i^{1/j_i})>c/q
for some positive constant c=c(y) and all q\in N. These sets are the `twisted'
inhomogeneous analogue of Bad(j_1,...,j_n) in the theory of simultaneous
Diophantine approximation. It has been shown that they have full Hausdorff
dimension in the nonweighted setting, i.e provided that j_i=1/n, and in the
weighted setting when x is chosen from Bad(j_1,...,j_n). We generalise these
results proving the full Hausdorff dimension in the weighted setting without
any condition on x.
Original language  English 

Number of pages  14 
Journal  Acta Arithmetica 
Volume  177 
Issue number  4 
Early online date  22 Feb 2017 
DOIs  
Publication status  Epub ahead of print  22 Feb 2017 
Bibliographical note
© Instytut Matematyczny PAN, 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