On the nonarchimedean quadratic Lagrange spectra

Mathematische Zeitschrift - Tập 294 - Trang 1065-1084 - 2019
Jouni Parkkonen1, Frédéric Paulin2
1Department of Mathematics and Statistics, Jyväskylä, Finland
2Laboratoire de mathématique d’Orsay, UMR 8628 Univ. Paris-Sud et CNRS, Université Paris-Saclay, ORSAY, France

Tóm tắt

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.

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Mathematische Zeitschrift

Tập 294

1065-1084

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