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Modular equations of a continued fraction of order six
- Title
- Modular equations of a continued fraction of order six
- Authors
- Lee, Yoonjin; Park, Yoon Kyung
- Ewha Authors
- 이윤진
- SCOPUS Author ID
- 이윤진
- Issue Date
- 2019
- Journal Title
- OPEN MATHEMATICS
- ISSN
- 2391-5455
- Citation
- OPEN MATHEMATICS vol. 17, pp. 202 - 219
- Keywords
- Ramanujan continued fraction; modular function; modular equation; ray class fields
- Publisher
- DE GRUYTER POLAND SP ZOO
- Indexed
- SCIE; SCOPUS
- Document Type
- Article
- Abstract
- We study a continued fraction X(tau) of order six by using the modular function theory. We first prove the modularity of X(tau), and then we obtain the modular equation of X(tau) of level n for any positive integer n; this includes the result of Vasuki et al. for n = 2, 3, 5, 7 and 11. As examples, we present the explicit modular equation of level p for all primes p less than 19. We also prove that the ray class field modulo 6 over an imaginary quadratic field K can be obtained by the value X-2 (tau). Furthermore, we show that the value 1/X(tau) is an algebraic integer, and we present an explicit procedure for evaluating the values of X(tau) for infinitely many tau's in K.
- DOI
- 10.1515/math-2019-0003
- Appears in Collections:
- 자연과학대학 > 수학전공 > Journal papers
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