科研之友
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摘要
Let k(n) (x) be the n-th partial quotient of the generalized continued fraction (GCF) expansion of a. This paper is concerned with the growth rate of k(n) (x). When the parameter function satisfies -1 < epsilon(k) <= 1, we obtain the Hausdorff dimension of the sets @@@ E phi = {x is an element of (0,1) : lim(n ->infinity) log k(n)(x)/phi(n) = 1} @@@ for any nondecreasing phi with lim(n ->infinity) (phi(n + 1) - phi(n)) = infinity and lim(n ->infinity) phi(n 1)/phi(n) = 1. Applications are given to several 91-400 kinds of exceptional sets related to the GCF expansion.
