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December 2008 Counting Diophantine Approximations
Jörg Brüdern
Funct. Approx. Comment. Math. 39(2): 237-260 (December 2008). DOI: 10.7169/facm/1229696574

Abstract

A recent development of the Davenport-Heilbronn method for diophantine inequalities is reexamined, and then applied to a class of problems in diophantine approximation. Among other things, an asymptotic formula is obtained for the number of solutions of the simultaneous inequalities $|n_j - \lambda_j n_0| <\varepsilon$ with square-free $n_j \in [1,N]$, whenever the positive real numbers $\lambda_1, \ldots, \lambda_r$ and $1$ are linearly independent over the rationals.

Citation

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Jörg Brüdern. "Counting Diophantine Approximations." Funct. Approx. Comment. Math. 39 (2) 237 - 260, December 2008. https://doi.org/10.7169/facm/1229696574

Information

Published: December 2008
First available in Project Euclid: 19 December 2008

zbMATH: 1211.11085
MathSciNet: MR2490739
Digital Object Identifier: 10.7169/facm/1229696574

Subjects:
Primary: 11J13
Secondary: 11D75

Keywords: Davenport-Heilbronn method , diophantine approximation , square-free numbers

Rights: Copyright © 2008 Adam Mickiewicz University

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Vol.39 • No. 2 • December 2008
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