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Independence of the Diophantine exponents associated with linear subspaces

Gaétan Guillot

Vol. 14 (2025), No. 3, 189–238
DOI: 10.2140/cnt.2025.14.189
Abstract

We elaborate on a problem raised by Schmidt in 1967 which generalizes the theory of classical Diophantine approximation to subspaces of n . We consider Diophantine exponents for linear subspaces of n which generalize the irrationality measure for real numbers. We prove here that we have no smooth relations among some functions associated to these exponents. To establish this result, we construct subspaces for which we are able to compute the exponents.

Keywords
Diophantine approximation, geometry of numbers
Mathematical Subject Classification
Primary: 11J13, 11J25
Secondary: 11J17
Milestones
Received: 11 June 2024
Accepted: 18 July 2025
Published: 6 September 2025
Authors
Gaétan Guillot
Université Paris-Saclay
CNRS, Laboratoire de mathématiques d’Orsay
Orsay
France