Continued fractions with bounded even-order partial quotients

被引：0
|
作者：
Hancl, Jaroslav [1 ]
Turek, Ondrej [1 ,2 ,3 ]
机构：
[1] Univ Ostrava, Dept Math, 30 Dubna 22, Ostrava 70103, Czech Republic
[2] Czech Acad Sci, Nucl Phys Inst, Hlavni 130, Rez 25068, Czech Republic
[3] Kochi Univ Technol, Lab Phys, Tosa Yamada, Kochi 7828502, Japan
来源：
RAMANUJAN JOURNAL | 2023年 / 62卷 / 01期
关键词：
Continued fraction; Bounded partial quotients; Sum of continued fractions; Product of continued fractions; Hausdorff dimension; HAUSDORFF DIMENSION; CANTOR SETS; NUMBERS; SUMS;
D O I：
10.1007/s11139-023-00741-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The paper is concerned with continued fractions having bounded even-order partial quotients. We demonstrate that every real number can be written as a sum of two continued fractions whose even-order partial quotients are equal to 1, and every positive number can be written as a product of two such continued fractions. Then we study the Hausdorff dimension of the set of continued fractions whose even-order partial quotients are all equal to a given positive integer c. Taking in particular c=1, we show that the set of continued fractions with even-order partial quotients equal to 1 has the Hausdorff dimension between 0.732 and 0.819.
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页码：69 / 110
页数：42
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