On evaluations of the cubic continued fraction by modular equations of degree 9

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2016, v.23 no.3, pp.223-236

https://doi.org/10.7468/jksmeb.2016.23.3.223

PAEK, DAE HYUN (DEPARTMENT OF MATHEMATICS EDUCATION, BUSAN NATIONAL UNIVERSITY OF EDUCATION)
YI, JINHEE (DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE, KOREA SCIENCE ACADEMY OF KAIST)

PAEK, DAE HYUN, & YI, JINHEE. (2016). ON EVALUATIONS OF THE CUBIC CONTINUED FRACTION BY A MODULAR EQUATION OF DEGREE 9. 한국수학교육학회지시리즈B:순수및응용수학, 23(3), 223-236, https://doi.org/10.7468/jksmeb.2016.23.3.223

복사

Abstract

We show how to evaluate the cubic continued fraction <TEX>$G(e^{-{\pi}\sqrt{n}})$</TEX> and <TEX>$G(-e^{-{\pi}\sqrt{n}})$</TEX> for n = 4m, 4−m, 2 · 4m, and 2−1 · 4−m for some nonnegative integer m by using modular equations of degree 9. We then find some explicit values of them.

keywords: continued fraction, modular equations, theta functions

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논문 상세

Vol.23 No.3

ON EVALUATIONS OF THE CUBIC CONTINUED FRACTION BY A MODULAR EQUATION OF DEGREE 9

On evaluations of the cubic continued fraction by modular equations of degree 9

Abstract

한국수학교육학회지시리즈B:순수및응용수학