논문KCI 등재
On Some Modular Equations and Their Applications I
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초록
We derive several modular equations and present their proofs based on concise algebraic computations. In addition, we establish ex- plicit relations and formulas for some parameterizations for the theta functions φ and φ and show some applications of the modular equations to evaluations of the cubic continued fraction and the theta function φ.
Abstract
We derive several modular equations and present their proofs based on concise algebraic computations. In addition, we establish ex- plicit relations and formulas for some parameterizations for the theta functions φ and φ and show some applications of the modular equations to evaluations of the cubic continued fraction and the theta function φ.
참고문헌 (9)
- B. C. Berndt, "Number Theory in the Spirit of Ramanujan" (2006), American Mathematical Society
- B. C. Berndt, "Ramanujan’s Notebooks, Part III" (1991), Springer–Verlag
- B. C. Berndt, "Ramanujan’s Notebooks, Part IV" (1994), Springer–Verlag
- H. H. Chan, "On Ramanujan’s cubic continued fraction", Acta Arith, 73, pp.343~355 (1995)
- R. A. Rankin, "Modular Forms and Functions" (1977), Cambridge University Press
- B. Schoeneberg, "Elliptic Modular Functions" (1974), Springer–Verlag
- J. Yi, "The Construction and Applications of Modular Equations", 박사, pp.2001
- J. Yi, "Theta-function identities and the explicit formulas for theta-function and their applications", J. Math. Anal. Appl, 292(2), pp.381~400 (2004)
- J. Yi, "The explicit formulas and evaluations of Ramanujan’s theta-function", J. Math. Anal. Appl, 321(1), pp.157~181 (2006)
관련 논문AI추천
On some modular equations and their applications II백대현, 이진희대한수학회 · 대한수학회보2013 · 제50권 제4호On some modular equations of degree 5 and their applications백대현, 이진희대한수학회 · 대한수학회보2013 · 제50권 제4호On Evaluations of the Cubic Continued Fraction by Modular Equations of Degree 3 Revisited백대현, 안지원, 이강훈, 이진희한국수학교육학회 · 이론수학과 교직수학2024 · 제31권 제2호On evaluations of the cubic continued fraction by modular equations of degree 9Dae Hyun Paek, Jinhee Yi한국수학교육학회 · 이론수학과 교직수학2016 · 제23권 제3호ON EVALUATIONS OF THE CUBIC CONTINUED FRACTION BY MODULAR EQUATIONS OF DEGREE 3Dae Hyun Paek, Jinhee Yi, Yong Jin Shin한국수학교육학회 · 이론수학과 교직수학2018 · 제25권 제1호On evaluations of the modular $j$--invariant by modular equations of degree 2Dae Hyun Paek, Jinhee Yi대한수학회 · 대한수학회보2015 · 제52권 제1호
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