Continued fractions of Laurent series with partial quotients from a given set

1. Introduction. Van der Poorten and Shallit's paper [10] begins: " It is notorious that it is damnably difficult to explicitly compute the continued fraction of a quantity presented in some other form ". The quantity is usually presented either as a power series or as the root of a specific equation. There has been some success in the former case for continued fractions of real numbers, such as Euler's famous continued fraction for e [11] and more recent work [10] on " folded " continued fractions; however, other than the well-known results for quadratic real numbers, the only success with the latter has been for continued fractions of Laurent series rather than real numbers. In this paper we continue this line of investigation. We consider families of continued fractions of Laurent series whose partial quotients all lie in a given set. Following ideas of Baum and Sweet [2], we show that one may describe the zeros of certain collections of equations in terms of such families. The paragraphs that follow introduce the notation and definitions necessary to give a fuller description of our results. Let F q be the finite field with q elements and L q denote the field of formal Laurent series in x