# Multiplicative parametric geometry of numbers and transference theorems for lattice exponents

## TL;DR

This paper extends the parametric geometry of numbers to a multiplicative framework, deriving new inequalities for lattice exponents that parallel classical transference inequalities in Diophantine approximation.

## Contribution

It introduces a multiplicative adaptation of parametric geometry of numbers and establishes a chain of inequalities for lattice exponents, refining classical transference results.

## Key findings

- Derived a chain of inequalities for multiplicative lattice exponents
- Split the transference inequality for Diophantine exponents
- Extended the framework of parametric geometry of numbers to multiplicative settings

## Abstract

In this paper we adapt parametric geometry of numbers developed by Wolfgang Schmidt and Leonard Summerer to a multiplicative setting, and derive a chain of inequalities for the corresponding exponents which splits the transference inequality for Diophantine exponents of lattices in the same way Khintchine's transference inequalities for simultaneous approximation can be split.