A UNIFIED CONTINUED FRACTION EXPANSION AND INDEPENDENCE CHARACTERIZATION

Abstract

An algorithm to construct a general continued fraction expansion for elements in a discrete-valued non-archimedean fields (K,|·|) is devised. Such continued fraction takes the form b1 a1+ b2 a2+ ··· bn an+ ···, where the elements an,bn are subject to the condition |an| > |bn|. Several examples are given to show that this algorithm yields almost all known continued fraction expansions as special cases. Criteria for algebraic and linear dependences of certain classes of such continued fractions are derived.