On Diophantine exponents of lattices

TL;DR

This paper characterizes the spectrum of Diophantine exponents for lattices in any dimension, simplifying the problem to the two-dimensional case using metric theory techniques.

Contribution

It provides a reduction of the Diophantine exponents spectrum problem to the two-dimensional case, advancing understanding of lattice approximation properties.

Findings

Spectrum of exponents described for all dimensions

Reduction to two-dimensional case

Uses metric theory arguments

Abstract

We describe the spectrum of ordinary Diophantine exponents for $d$-dimensional lattices. The result reduces the problem to two-dimensional case and uses argument of metric theory.