SOME RESULTS ON THE LARGEST PARTIAL QUOTIENT IN CONTINUED FRACTIONS

Abstract

Let [Formula: see text] be a function satisfying [Formula: see text] as [Formula: see text]. Write [Formula: see text] where [Formula: see text] denotes the largest partial quotient among the first [Formula: see text] terms in the continued fraction expansion of [Formula: see text]. We prove that [Formula: see text] has full Hausdorff dimension for a large class of functions [Formula: see text], which strengthens the result of [L. Fang and J. Liu, On the largest partial quotients in continued fraction expansions, Fractals 29 (2021) 2150099.].