(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 5, PAGES 93-101

## On inhomogeneous Diophantine approximation and Hausdorff dimension

M. Laurent

Abstract

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Let G =ZA+Zn Ì Rn be a dense subgroup of rank $n+1$ and let $\hat \left\{\omega \right\}\left(A\right)$ denote the exponent of uniform simultaneous rational approximation to the generating point $A$. For any real number $v\geq \hat \left\{\omega \right\}\left(A\right)$, the Hausdorff dimension of the set $B$v of points in Rn that are $v$-approximable with respect to G is shown to be equal to $1/v$.

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