On the nonarchimedean quadratic Lagrange spectra
Abstract
We study Diophantine approximation in completions of functions fields over finite fields, and in particular in fields of formal Laurent series over finite fields. We introduce a Lagrange spectrum for the approximation by orbits of quadratic irrationals under the modular group. We give nonarchimedean analogs of various well known results in the real case: the closedness and boundedness of the Lagrange spectrum, the existence of a Hall ray, as well as computations of various Hurwitz constants. We use geometric methods of group actions on Bruhat-Tits trees.
Main Authors
Format
Articles
Research article
Published
2020
Series
Subjects
Publication in research information system
Publisher
Springer Berlin Heidelberg
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202003252548Use this for linking
Review status
Peer reviewed
ISSN
0025-5874
DOI
https://doi.org/10.1007/s00209-019-02300-1
Language
English
Published in
Mathematische Zeitschrift
Citation
- Parkkonen, J., & Paulin, F. (2020). On the nonarchimedean quadratic Lagrange spectra. Mathematische Zeitschrift, 294(3-4), 1065-1084. https://doi.org/10.1007/s00209-019-02300-1
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Additional information about funding
This work was supported by the French-Finnish CNRS grant PICS No 6950.
Copyright© Springer-Verlag GmbH Germany, part of Springer Nature 2019