The relative growth rate of the largest partial quotient to the sum of partial quotients in continued fraction expansions

摘要

In this paper, we mainly study the growth rate of the largest partial quotient relative to the growth rate of the sum of partial quotients for the continued fraction expansion of an irrational number. We establish that the Hausdorff dimension of the set of points with a given relative growth rate is full. (c) 2016 Elsevier Inc. All rights reserved.