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2019 Generalized simultaneous approximation to $m$ linearly dependent reals
Leonhard Summerer
Mosc. J. Comb. Number Theory 8(3): 219-228 (2019). DOI: 10.2140/moscow.2019.8.219

Abstract

In order to analyse the simultaneous approximation properties of m reals, the parametric geometry of numbers studies the joint behaviour of the successive minima functions with respect to a one-parameter family of convex bodies and a lattice defined in terms of the m given reals. For simultaneous approximation in the sense of Dirichlet, the linear independence over of these reals together with 1 is equivalent to a certain nice intersection property that any two consecutive minima functions enjoy. This paper focusses on a slightly generalized version of simultaneous approximation where this equivalence is no longer in place and investigates conditions for that intersection property in the case of linearly dependent irrationals.

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Leonhard Summerer. "Generalized simultaneous approximation to $m$ linearly dependent reals." Mosc. J. Comb. Number Theory 8 (3) 219 - 228, 2019. https://doi.org/10.2140/moscow.2019.8.219

Information

Received: 17 October 2018; Revised: 20 March 2019; Accepted: 22 May 2019; Published: 2019
First available in Project Euclid: 13 August 2019

zbMATH: 07095941
MathSciNet: MR3990805
Digital Object Identifier: 10.2140/moscow.2019.8.219

Subjects:
Primary: 11H06, 11J13

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.8 • No. 3 • 2019
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