RAMANUJAN CONTINUED FRACTIONS OF ORDER EIGHTEEN

被引：0
|
作者：
Park, Yoon Kyung [1 ]
机构：
[1] Seoul Natl Univ Sci & Technol, Sch Nat Sci, Seoul 01811, South Korea
来源：
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2023年 / 60卷 / 02期
关键词：
Ramanujan continued fraction; modular function; Klein forms; EQUATIONS;
D O I：
10.4134/JKMS.j220180
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
As an analogy of the Rogers-Ramanujan continued fraction, we define a Ramanujan continued fraction of order eighteen. There are essentially three Ramanujan continued fractions of order eighteen, and we study them using the theory of modular functions. First, we prove that they are modular functions and find the relations with the Ramanujan cubic continued fraction C(t). We can then obtain that their values are algebraic numbers. Finally, we evaluate them at some imaginary quadratic quantities.
引用
收藏
页码：395 / 406
页数：12
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