Heriot-Watt Mathematics Report Series
HWM97-39, 22 October 1997
The Hausdorff dimension of sets arising from simultaneous Diophantine approximation with different error terms in each inequality
B P Rynne
Abstract
Suppose that $m$ is a positive integer, $\mbox{\boldmath$\tau$} = (\tau_1,\dots,\tau_m) \in R^m$
is a vector of strictly positive numbers,
and $Q$ is an infinite set of positive integers.
Let $W_Q(m;\mbox{\boldmath$\tau$})$ be the set
$$
\{ x} \in R^{m} :
\|x_{i} q \| < q^{-\tau_i} , \ 1 \le i \le m,\
\mbox{for infinitely many } q \in Q \}.
$$
In this paper we obtain the Hausdorff dimension of this set.
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Full text: http://www.ma.hw.ac.uk/~bryan/ps_files/differrtrms.ps.Z
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