Parametric geometry of numbers in function fields
Number Theory
2019-05-07 v2
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.
Cite
@article{arxiv.1704.00291,
title = {Parametric geometry of numbers in function fields},
author = {Damien Roy and Michel Waldschmidt},
journal= {arXiv preprint arXiv:1704.00291},
year = {2019}
}
Comments
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