Groupe modulaire, fractions continues et approximation diophantienne en caractéristique p
Tóm tắt
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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