On the nonarchimedean quadratic Lagrange spectra
Parkkonen, J., & Paulin, F. (2020). On the nonarchimedean quadratic Lagrange spectra. Mathematische Zeitschrift, 294 (3-4), 1065-1084. doi:10.1007/s00209-019-02300-1
Published inMathematische Zeitschrift
© Springer-Verlag GmbH Germany, part of Springer Nature 2019
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.