2018/01/24 by Jouni Parkkonen, Parkkonen, Jouni, Paulin, Frédéric
Computer Science · Mathematics · #11J06 #11J70 #11R11 #20E08 #20G25 #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #advanced mathematical theories
paper · doi:10.48550/arxiv.1801.08046
openalex publication_date 2018/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.