Vol. 11, No. 1, 2022

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On a conjecture of N. Moshchevitin

Leonhard Summerer

Vol. 11 (2022), No. 1, 115–124
Abstract

This paper is devoted to the proof of a conjecture of N. Moshchevitin related to the study of the approximation properties of badly approximable vectors. The proof uses the parametric geometry of numbers and relies on a fundamental theorem of D. Roy.

Keywords
badly approximable vectors, simultaneous approximation
Mathematical Subject Classification
Primary: 11H06, 11J13
Milestones
Received: 26 November 2021
Revised: 9 December 2021
Accepted: 23 December 2021
Published: 30 March 2022
Authors
Leonhard Summerer
Faculty of Mathematics
University of Vienna
Vienna
Austria