Parametric geometry of numbers in function fields

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.

20 pages, the proof of a central lemma is simplified and the main construction is shown to be universal. This paper will appear in Mathematika

References in corpus (1)

• On Schmidt and Summerer parametric geometry of numbers

Cited by in corpus (2)

• A variational principle in the parametric geometry of numbers
• On the maximum size of ultrametric orthogonal sets over discrete valued fields