Projects per year
Abstract
Let $\mathcal{D}=(d_n)_{n=1}^\infty$ be a bounded sequence of integers with $d_n\ge 2$ and let $(i, j)$ be a pair of strictly positive numbers with $i+j=1$. We prove that the set of $x \in \RR$ for which there exists some constant $c(x) > 0$ such that \[ \max\{q_\DDD^{1/i}, \qx\^{1/j}\} > c(x)/ q \qquad \forall q \in \NN \] is one quarter winning (in the sense of Schmidt games). Thus the intersection of any countable number of such sets is of full dimension. In turn, this establishes the natural analogue of Schmidt's conjecture within the framework of the de MathanTeuli\'e conjecture  also known as the `Mixed Littlewood Conjecture'.
Original language  English 

Pages (fromto)  239245 
Number of pages  6 
Journal  Mathematika 
Volume  57 
Issue number  2 
DOIs  
Publication status  Published  Jul 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