Increasing rate of weighted product of partial quotients in continued fractions

Ayreena Bakhtawar and Jing Feng

Chaos, Solitons & Fractals, 2023, vol. 172, issue C

Abstract: Let [a1(x),a2(x),…,an(x),…] be the continued fraction expansion of x∈[0,1). In this paper, we study the increasing rate of the weighted product ant0(x)an+1t1(x)⋯an+mtm(x) ,where ti∈R+(0≤i≤m) are weights. More precisely, let φ:N→R+ be a function with φ(n)/n→∞ as n→∞. For any (t0,…,tm)∈R+m+1 with ti≥0 and at least one ti≠0(0≤i≤m), the Hausdorff dimension of the set E̲({ti}i=0m,φ)=x∈[0,1):lim infn→∞logant0(x)an+1t1(x)⋯an+mtm(x)φ(n)=1 is obtained. Under the condition that (t0,…,tm)∈R+m+1 with 0Keywords: Continued fractions; Hausdorff dimension; Product of partial quotients (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:172:y:2023:i:c:s0960077923004927

DOI: 10.1016/j.chaos.2023.113591

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