Abstract
Let L be a function field of a hyperelliptic curve defined over an arbitrary field characteristic different from 2. We construct an arithmetic of continued fractions of an arbitrary quadratic irrationality in field of formal power series with respect to linear finite valuation. The set of infinite valuation and finite linear valuation of L is denoted by S. As an application, we have found a relationship between the issue of the existence of nontrivial S-units in L and periodicity of continued fractions of some key elements of L.
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