Modular equations of a continued fraction of order six
- 주제(키워드) Ramanujan continued fraction , modular function , modular equation , ray class fields
- 주제(기타) Mathematics
- 설명문(일반) [Lee, Yoonjin] Ewha Womans Univ, Dept Math, 52 Seodaemun Gu, Seoul 03760, South Korea; [Park, Yoon Kyung] Gongju Natl Univ Educ, Dept Math Educ, 27 Ungjin Ro, Gongju Si 32553, Chungcheongnam, South Korea
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- OA유형 gold
- 발행기관 DE GRUYTER POLAND SP ZOO
- 발행년도 2019
- URI http://www.dcollection.net/handler/ewha/000000160093
- 본문언어 영어
- Published As http://dx.doi.org/10.1515/math-2019-0003
초록/요약
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.
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