On triviality of uniform Diophantine exponents of lattices

TL;DR

This paper proves that the uniform Diophantine exponents of lattices can only take trivial values, highlighting a fundamental limitation in their approximation properties.

Contribution

It establishes that the uniform Diophantine exponents of lattices are always trivial, providing a definitive result in the theory of Diophantine approximation.

Findings

Uniform Diophantine exponents are always trivial for lattices.

The result applies broadly to all lattices, indicating a fundamental property.

This work clarifies the limitations of Diophantine approximation in lattice theory.

Abstract

In this paper we prove that uniform Diophantine exponents of lattices attain only trivial values.