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Mosc. Math. J., 2005, Volume 5, Number 4, Pages 747–766 (Mi mmj220)  

This article is cited in 40 scientific papers (total in 40 papers)

On exponents of homogeneous and inhomogeneous Diophantine approximation

Ya. Bugeauda, M. Laurentb

a University Louis Pasteur
b Institut de Mathématiques de Luminy

Abstract: In Diophantine Approximation, inhomogeneous problems are linked with homogeneous ones by means of the so-called Transference Theorems. We revisit this classical topic by introducing new exponents of Diophantine approximation. We prove that the inhomogeneous exponent of approximation to a generic point in $\mathbb R^n$ by a system of $n$ linear forms is equal to the inverse of the uniform homogeneous exponent associated to the system of dual linear forms.

Key words and phrases: Diophantine approximation, measures of homogeneous and inhomogeneous approximation, uniform exponents, spectra.


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MSC: 11J20, 11J13, 11J82
Received: November 4, 2004

Citation: Ya. Bugeaud, M. Laurent, “On exponents of homogeneous and inhomogeneous Diophantine approximation”, Mosc. Math. J., 5:4 (2005), 747–766

Citation in format AMSBIB
\by Ya.~Bugeaud, M.~Laurent
\paper On exponents of homogeneous and inhomogeneous Diophantine approximation
\jour Mosc. Math.~J.
\yr 2005
\vol 5
\issue 4
\pages 747--766

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    This publication is cited in the following articles:
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    20. Shapira U., “Grids with Dense Values”, Comment. Math. Helv., 88:2 (2013), 485–506  crossref  mathscinet  zmath  isi  scopus
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    30. Bengoechea P., Moshchevitin N., “Badly Approximable Points in Twisted Diophantine Approximation and Hausdorff Dimension”, Acta Arith., 177:4 (2017), 301–314  crossref  zmath  isi  scopus
    31. Ghosh A., Gorodnik A., Nevo A., “Best Possible Rates of Distribution of Dense Lattice Orbits in Homogeneous Spaces”, J. Reine Angew. Math., 745 (2018), 155–188  crossref  mathscinet  zmath  isi  scopus
    32. Fukshansky L., Moshchevitin N., “On An Effective Variation of Kronecker'S Approximation Theorem Avoiding Algebraic Sets”, Proc. Amer. Math. Soc., 146:10 (2018), 4151–4163  crossref  mathscinet  zmath  isi  scopus
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    35. Johannes Schleischitz, “Diophantine approximation in prescribed degree”, Mosc. Math. J., 18:3 (2018), 491–516  mathnet  crossref
    36. Kim D.H., Liao L., “Dirichlet Uniformly Well-Approximated Numbers”, Int. Math. Res. Notices, 2019:24 (2019), 7691–7732  crossref  mathscinet  isi
    37. Chow S., Technau N., “Higher-Rank Bohr Sets and Multiplicative Diophantine Approximation”, Compos. Math., 155:11 (2019), 2214–2233  crossref  mathscinet  zmath  isi
    38. Bugeaud Ya., Zhang Zh., “on Homogeneous and Inhomogeneous Diophantine Approximation Over the Fields of Formal Power Series”, Pac. J. Math., 302:2 (2019), 453–480  crossref  mathscinet  zmath  isi  scopus
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