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On homogeneous and
inhomogeneous Diophantine approximation over the fields of
formal power series
Yann Bugeaud and Zhenliang Zhang |
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Vol. 302 (2019), No. 2, 453–480
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Abstract |
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We prove over fields of power series the analogues of several Diophantine approximation results obtained over the field of real numbers. In particular we establish the power series analogue of Kronecker’s theorem for matrices, together with a quantitative form of it, which can also be seen as a transference inequality between uniform approximation and inhomogeneous approximation. Special attention is devoted to the one-dimensional case. Namely, we give a necessary and sufficient condition on an irrational power series which ensures that, for some positive , the set has full Hausdorff dimension. |
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Keywords
Diophantine approximation, power series field, exponent of
homogeneous approximation, exponent of inhomogeneous
approximation, Hausdorff dimension
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Mathematical Subject Classification 2010
Primary: 11K55
Secondary: 11J04, 28A80
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Milestones
Received: 10 January 2019
Revised: 28 March 2019
Accepted: 1 April 2019
Published: 27 November 2019
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Authors |
| Yann Bugeaud | |
| IRMA UMR 7501 Université de Strasbourg, CNRS Strasbourg France |
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| Zhenliang Zhang | |
| School of Mathematical
Sciences Henan Institute of Science and Technology Xinxiang China |
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