Let k be an imaginary quadratic field, h the complex upper half plane, and let tau is an element of h boolean AND k, p = e(piitau). In this article, using the infinite product formulas for g(2) and g(3), we prove that values of certain infinite products are transcendental whenever tau are imaginary quadratic. And we derive analogous results of Berndt-Chan-Zhang ([4]). Also we find the values of Pi(n=1)(infinity)(1-p(2n-1)/1+p(2n-1))(8) and pPi(n=1)(infinity) (1 + p(2n))(12) when we know j (tau). And we construct an elliptic curve E : y(2) = x(3) + 3x(2) + (3 - j/2563)x + 1 with i = j(tau) not equal 0 and P = (16(2)P(2) Pi(n=1)(infinity)(1 + p(2n)) (24), 0) is an element of E.

- Publisher
- KOREAN MATHEMATICAL SOC

- Issue Date
- 2003-11

- Language
- English

- Article Type
- Article

- Citation
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, v.40, no.6, pp.977 - 998

- ISSN
- 0304-9914

- Appears in Collection
- MA-Journal Papers(저널논문)

- Files in This Item
- There are no files associated with this item.

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.