Moscow Mathematical Journal

Volume 25, Issue 1, January–March 2025 pp. 33–61.

On Geometry of Simultaneous Approximation to Three Real Numbers

Authors: Antoine Marnat (1) and Nikolay Moshchevitin (2)
Author institution:(1) Univ. Paris Est Créteil, Univ. Gustave Eiffel, CNRS, LAMA UMR8050, F-94010 Créteil, France
Institut für Diskrete Mathematik und Geometrie, TU Wien, Wien, Austria
(2) Technische Universität Wien
Faculty of Computer Science, HSE University, Pokrovsky boulevard 11, Moscow, Russia 109028
Moscow Center of Fundamental and Applied Mathematics

Summary:

Considering simultaneous approximation to three numbers, we study the geometry of the sequence of the best approximations. We provide a sharper lower bound for the ratio of ordinary and uniform exponent of Diophantine approximation, optimal in terms of this geometry.

2020 Math. Subj. Class. 11J13.

Keywords: Simultaneous approximation, Diophantine exponents, best approximations.

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