Abstract
The aim of this paper is to give a geometric interpretation of the continued fraction expansion in the field \(\hat K = \mathbb{F}_q ((X^{ - 1} ))\) of formal Laurent series in X −1 over \(\mathbb{F}_q \), in terms of the action of the modular group \({\text{SL}}_{\text{2}} (\mathbb{F}_q [X])\) on the Bruhat–Tits tree of \({\text{SL}}_{\text{2}} (\hat K)\), and to deduce from it some corollaries for the diophantine approximation of formal Laurent series in X −1 by rational fractions in X.
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Paulin, F. Groupe modulaire, fractions continues et approximation diophantienne en caractéristique p . Geometriae Dedicata 95, 65–85 (2002). https://doi.org/10.1023/A:1021270631563
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DOI: https://doi.org/10.1023/A:1021270631563