논문KCI 등재
On evaluations of the modular $j$--invariant by modular equations of degree 2
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We derive modular equations of degree 2 to establish explicit relations for the parameterizations for the theta functions $\varphi$ and $\psi$. We then find specific values of the parameterizations to evaluate some new values of the modular $j$--invariant in terms of $J_n$.
Abstract
We derive modular equations of degree 2 to establish explicit relations for the parameterizations for the theta functions $\varphi$ and $\psi$. We then find specific values of the parameterizations to evaluate some new values of the modular $j$--invariant in terms of $J_n$.
참고문헌 (8)
- B. C. Berndt, "Ramanujan’s Notebooks. Part V" (1998), Springer–Verlag
- B. C. Berndt, "Ramanujan’s Notebooks. Part III" (1991), Springer–Verlag
- B. C. Berndt, "Number Theory in the Spirit of Ramanujan" (2006), American Mathematical Society
- B. C. Berndt, "Ramanujan and the modular j–invariant", Canad. Math. Bull, 42(4), pp.427~440 (1999)
- D. A. Cox, "Primes of the Form x2 + ny2" (1989), Wiley
- J. Yi, "The Construction and Applications of Modular Equations", Ph.D., 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 ψ", J. Math. Anal. Appl, 321(1), pp.157~181 (2006)
관련 논문AI추천
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