What question did this study set out to answer?

The aim is to explore the multifractal spectrum related to the convergence exponents of weighted products of partial quotients in continued fractions.

February 22, 2026

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

Key Points

The aim is to explore the multifractal spectrum related to the convergence exponents of weighted products of partial quotients in continued fractions.
Analysis of continued fraction expansions
Mathematical derivation of multifractal spectra
Examination of weighted products of partial quotients
Identified specific convergence exponents for weighted products
Described the multifractal spectrum characteristics
Extended discussion on products of more than two partial quotients

Abstract

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 is also discussed.

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