# Parametric geometry of numbers in function fields

## TL;DR

This paper extends the parametric geometry of numbers, a recent theory in Diophantine approximation, to function fields, and applies it to analyze simultaneous approximation of exponential functions.

## Contribution

It introduces a novel adaptation of the parametric geometry of numbers to function fields and explores its application to exponential function approximation.

## Key findings

- Extended the theory to function fields of rational functions.
- Provided new insights into simultaneous approximation of exponential functions.
- Simplified classical Diophantine approximation problems.

## Abstract

Parametric geometry of numbers is a new theory, recently created by Schmidt and Summerer, which unifies and simplifies many aspects of classical Diophantine approximations, providing a handle on problems which previously seemed out of reach. Our goal is to transpose this theory to fields of rational functions in one variable and to analyze in that context the problem of simultaneous approximation to exponential functions.