On convergence exponents of the weighted products of consecutive partial quotients in continued fractions

Let [Formula: see text] be the continued fraction expansion of [Formula: see text]. In this paper, for any [Formula: see text], we study the multifractal spectrum of the convergence exponent of the weighted product of consecutive partial quotients [Formula: see text] defined by [Formula: see text] The weighted products of more than two consecutive partial quotients are also discussed.