Convergence results for Oppenheim expansions (II)

Abstract

Under the framework of Giuliano (Monatsh Math 187:509-530, 2018) , we continue to study the quantity R n introduced in [11]. The goal of this paper is to find conditions such that R −1 n converges in distribution, n k=1 log R k satisfies the central limit theorem and the large deviation. We cover and expand a number of particular cases in the literature on Oppenheim series and Oppenheim continued fractions.