Two estimates concerning classical diophantine approximation constants (Q2875443)
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scientific article; zbMATH DE number 6330560
| Language | Label | Description | Also known as |
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| English | Two estimates concerning classical diophantine approximation constants |
scientific article; zbMATH DE number 6330560 |
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Two estimates concerning classical diophantine approximation constants (English)
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14 August 2014
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Diophantine approximation
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lattices
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approximation constants
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convex geometry
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The author investigates classical approximation constants concerning simultaneous diophantine approximation \(| \zeta^j x - y_j | \) with \(1 \leq j \leq n\), and concerning approximation with algebraic numbers of degree \(\leq n\). The paper contains new proofs of classical results of \textit{H. Davenport} and \textit{W. M. Schmidt} [Acta Arith. 15, 393--416 (1969; Zbl 0186.08603)] based on interesting geometric estimates. Furthermore, the author observes a certain uniformity of the bounds with respect to \(\zeta\).
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