Bibliographic Details
| Title: |
Comparing regular and backward continued fractions: Lochs-type theorems and approximation properties. |
| Authors: |
Tian, Zhigang1 (AUTHOR) 202010106099@mail.scut.edu.cn, Fang, Lulu1,2 (AUTHOR) fanglulu@njust.edu.cn |
| Source: |
Journal of Number Theory. Mar2026, Vol. 280, p947-972. 26p. |
| Subjects: |
Continued fractions, Approximation theory, Mathematical expansion, Mathematics theorems, Baire spaces, Lebesgue measure, Irrational numbers |
| Abstract: |
In this paper, we study two problems concerning the relationship between regular continued fractions (RCFs) and backward continued fractions (BCFs). The first problem addresses Lochs-type theorems for RCFs and BCFs, where we compare the number of partial quotients in one expansion as a function of the number of partial quotients in the other expansion. The second problem investigates the approximation properties of RCFs and BCFs, with particular attention to the set of irrational numbers that are infinitely often better approximated by BCFs than by RCFs. We show that this set has Lebesgue measure zero and further analyze it from the perspectives of Baire category and fractal dimension. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
