On the Quantitative Metric Theory of Continued Fractions in Positive Characteristic

摘要

Let q be the finite field of q elements. An analogue of the regular continued fraction expansion for an element α in the field of formal Laurent series over q is given uniquely by where is a sequence of polynomials with coefficients in q such that deg(A n (α)) 1 for all n1. In this paper, we provide quantitative versions of metrical results regarding averages of partial quotients. A sample result we prove is that, given any ? 0, we have for almost everywhere α with respect to Haar measure.