Construction of some continued fractions in discrete valued fields

Abstract

An algorithm for constructing continued fraction expansions of elements in a discrete valued field is established. Several examples are given to show that our algorithm yields almost all known continued fraction expansions as special cases. We derive criteria for algebraic and linear independence of elements in the function field with respect to a prime-adic valuation and sufficient conditions for algebraic and linear Independence of certain classes of continued fraction expan-sions. In the last part. We give explicit formulae for continued fraction expansions of some elements related to the exponential element in the function field with respect to the degree valuation. The main tool called the Folding Lemma, used in the construction of such explicit formulae is of major interest. Here we generalize this lemma and derive several applications.