A CONTINUED FRACTION OF ORDER TWELVE AS A MODULAR FUNCTION
- 주제(키워드) Ramanujan continued fraction , modular function
- 주제(기타) Mathematics, Applied
- 설명문(일반) [Lee, Yoonjin] Ewha Womans Univ, Dept Math, Seoul 03760, South Korea; [Park, Yoon Kyung] Ewha Womans Univ, Inst Math Sci, Seoul 03760, South Korea
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 AMER MATHEMATICAL SOC
- 발행년도 2018
- URI http://www.dcollection.net/handler/ewha/000000151632
- 본문언어 영어
- Published As http://dx.doi.org/10.1090/mcom/3259
초록/요약
We study a continued fraction U(tau) of order twelve using the modular function theory. We obtain the modular equations of U(tau) by computing the affine models of modular curves X(Gamma) with Gamma = Gamma(1)(12) boolean AND Gamma(0)(12n) for any positive integer n; this is a complete extension of the previous result of Mahadeva Naika et al. and Dharmendra et al. to every positive integer n. We point out that we provide an explicit construction method for finding the modular equations of U(tau). We also prove that these modular equations satisfy the Kronecker congruence relations. Furthermore, we show that we can construct the ray class field modulo 12 over imaginary quadratic fields by using U(tau) and the value U(tau) at an imaginary quadratic argument is a unit. In addition, if U(tau) is expressed in terms of radicals, then we can express U(r tau) in terms of radicals for a positive rational number r.
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