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Fundam. Prikl. Mat., 2010, Volume 16, Issue 5, Pages 93–101 (Mi fpm1340)  

On inhomogeneous Diophantine approximation and Hausdorff dimension

M. Laurent

Institut de Mathématiques de Luminy, France

Abstract: 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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English version:
Journal of Mathematical Sciences (New York), 2012, 180:5, 592–598

Bibliographic databases:

UDC: 511.72

Citation: M. Laurent, “On inhomogeneous Diophantine approximation and Hausdorff dimension”, Fundam. Prikl. Mat., 16:5 (2010), 93–101; J. Math. Sci., 180:5 (2012), 592–598

Citation in format AMSBIB
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\by M.~Laurent
\paper On inhomogeneous Diophantine approximation and Hausdorff dimension
\jour Fundam. Prikl. Mat.
\yr 2010
\vol 16
\issue 5
\pages 93--101
\mathnet{http://mi.mathnet.ru/fpm1340}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2804895}
\elib{https://elibrary.ru/item.asp?id=16349303}
\transl
\jour J. Math. Sci.
\yr 2012
\vol 180
\issue 5
\pages 592--598
\crossref{https://doi.org/10.1007/s10958-012-0658-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84855841078}


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