Intermediate Diophantine exponents and parametric geometry of numbers

TL;DR

This paper introduces intermediate Diophantine exponents and refines transference inequalities, advancing the understanding of Diophantine approximation through parametric geometry of numbers.

Contribution

It defines new intermediate exponents and decomposes classical inequalities into a chain, building on Schmidt and Summerer's ideas.

Findings

Defined intermediate Diophantine exponents.

Decomposed transference inequalities into a chain.

Extended the framework of parametric geometry of numbers.

Abstract

This is a revised compilation of the papers arXiv:1105.1554 and arXiv:1105.5823. We develop some of the ideas belonging to W.Schmidt and L.Summerer to define intermediate Diophantine exponents and split several transference inequalities into a chain of inequalities for intermediate exponents.