Diophantine exponents of lattices

TL;DR

This paper introduces Diophantine exponents for lattices, explores their properties, and establishes inequalities, using Schmidt's subspace theorem to construct illustrative examples.

Contribution

It defines a new concept of Diophantine exponents for lattices and proves foundational inequalities, advancing the understanding of lattice approximation properties.

Findings

Established transference inequalities for Diophantine exponents

Constructed examples using Schmidt's subspace theorem

Provided initial properties and framework for future research

Abstract

In this paper we define Diophantine exponents of lattices and investigate some of their properties. We prove transference inequalities and construct some examples with the help of Schmidt's subspace theorem.