본문 바로가기
KERD
논문KCI 등재

On some modular equations of degree 5 and their applications

0

조회

0

다운로드

2

인용

0

참고문헌

키워드

주제분류수학

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)

  1. B. C. Berndt, "Number Theory in the Spirit of Ramanujan" (2006), American Mathematical Society
  2. B. C. Berndt, "Ramanujan’s Notebooks, Part III" (1991), Springer–Verlag
  3. B. C. Berndt, "Ramanujan’s Notebooks, Part IV" (1991), Springer–Verlag
  4. B. C. Berndt, "Explicit Evaluations of the Rogers- Ramanujan continued fraction", J. Reine Angew. Math, 480, pp.141~159 (1996)
  5. B. C. Berndt, "Ramanujan: Essays and Surveys" (2001), American Mathematical Society
  6. 백대현, "On some modular equations and their applications II", 대한수학회보, 50(4), pp.1221~1233 (2013), 대한수학회
  7. R. A. Rankin, "Modular Forms and Functions" (1977), Cambridge University Press
  8. B. Schoeneberg, "Elliptic Modular Functions" (1974), Springer–Verlag
  9. J. Yi, "The Construction and Applications of Modular Equations", 박사, pp.2001
  10. J. Yi, Evaluations of the Rogers-Ramanujan continued fraction R(q)by modular equa-tions, Acta Arith. 97, "no. 2", 103–127 (2001)
  11. 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)
  12. 백대현, "On Some Modular Equations and Their Applications I", 대한수학회보, 50(3), pp.761~776 (2013), 대한수학회
  13. J. Yi, "The explicit formulas and evaluations of Ramanujan’s theta-function", J. Math. Anal. Appl, 321(1), pp.157~181 (2006)

관련 논문AI추천

이 간행물의 다른 논문 (27건)