Geodesic
On inhomogeneous Diophantine approximation and Hausdorff dimension
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 5, pp. 93-101 
M. Laurent. On inhomogeneous Diophantine approximation and Hausdorff dimension. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 5, pp. 93-101. http://geodesic.mathdoc.fr/item/FPM_2010_16_5_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\Gamma=\mathbf ZA+\mathbf Z^n\subset\mathbf R^n$ be a dense subgroup of rank $n+1$ and let $\hat\omega(A)$ denote the exponent of uniform simultaneous rational approximation to the generating point $A$. For any real number $v\ge\hat\omega(A)$, the Hausdorff dimension of the set $\mathcal B_v$ of points in $\mathbf R^n$ that are $v$-approximable with respect to $\Gamma$ is shown to be equal to $1/v$.

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