On some modular equations of degree 5 and their applications
0
조회
0
다운로드
2
인용
0
참고문헌
키워드
초록
We first derive several modular equations of degree 5 and present their concise proofs based on algebraic computations. We then establish explicit relations and formulas for some parameterizations for the theta functions φ and ψ by using the derived modular equations. In addition, we find specific values of the parameterizations and evaluate some numerical values of the Rogers-Ramanujan continued fraction.
Abstract
We first derive several modular equations of degree 5 and present their concise proofs based on algebraic computations. We then establish explicit relations and formulas for some parameterizations for the theta functions φ and ψ by using the derived modular equations. In addition, we find specific values of the parameterizations and evaluate some numerical values of the Rogers-Ramanujan continued fraction.
참고문헌 (13)
- 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" (1991), Springer–Verlag
- B. C. Berndt, "Explicit Evaluations of the Rogers- Ramanujan continued fraction", J. Reine Angew. Math, 480, pp.141~159 (1996)
- B. C. Berndt, "Ramanujan: Essays and Surveys" (2001), American Mathematical Society
- 백대현, "On some modular equations and their applications II", 대한수학회보, 50(4), pp.1221~1233 (2013), 대한수학회
- 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, Evaluations of the Rogers-Ramanujan continued fraction R(q)by modular equa-tions, Acta Arith. 97, "no. 2", 103–127 (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)
- 백대현, "On Some Modular Equations and Their Applications I", 대한수학회보, 50(3), pp.761~776 (2013), 대한수학회
- J. Yi, "The explicit formulas and evaluations of Ramanujan’s theta-function", J. Math. Anal. Appl, 321(1), pp.157~181 (2006)
