Renewal-type Limit Theorem for Continued Fractions with Even Partial Quotients

2008/02/29 by Francesco Cellarosi, Cellarosi, Francesco
Economics, Econometrics and Finance · Mathematics · #11J70 #11K50 (Primary) #28D05 #37E05 #60F99 #60K05 (Secondary) #Analytic Number Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.0802.4459

openalex publication_date 2008/02/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the existence of the limiting distribution for the sequence of denominators generated by continued fraction expansions with even partial quotients, which were introduced by F. Schweiger and studied also by C. Kraaikamp and A. Lopes. Our main result is proven following the strategy used by Ya. Sinai and C. Ulcigrai in their proof of a similar renewal-type theorem for Euclidean continued fraction expansions and the Gauss map. The main steps in our proof are the construction of a natural extension of a Gauss-like map and the proof of mixing of a related special flow.

Related

• Renewal-type Limit Theorem for the Gauss Map and Continued Fractions
• On certain statistical properties of continued fractions with even and with odd partial quotients
• Continued fractions with odd partial quotients
• Some asymptotic results for the continued fraction expansions with odd partial quotients
• On the distribution of partial quotients of reduced fractions with fixed denominator