# TRANSCENDENTAL NUMBERS AS VALUES OF ELLIPTIC FUNCTIONS

• Kim, Daeyeoul (Department of Mathematics, Chonbuk National University) ;
• Koo, Ja-Kyung (Korea Advanced Institute of Science and Technology, Department of Mathematics)
• Published : 2000.11.01

#### Abstract

As a by-product of [4], we give algebraic integers of certain values of quotients of Weierstrass $\delta'(\tau),\delta'(\tau)$-functions. We also show that special values of elliptic functions are transcendental numbers.

#### References

1. Proc. Edinburgh Math. Soc. v.40 Ramanujan's remarkable product of theta-functions B. C. Burndt;H. H. Chan;L. -C. Zhang
2. Grundlehren der mathematichen wissenschaften v.281 Elliptic Functions K. Chandrasekharan
3. Mathematische Wreke v.2 Uber die Entwicklungskoeffizienten der lemniscatischen Funktionen A. Hurwiz
4. Algebraic integers as values of elliptic functions D. Kim;J. Koo
5. Elliptic Functions S. Lang
6. Mat. Sb. v.187 Modular funtions and transcendence problems Y. Nesterenko
7. Trans. Cambr. Phil. Soc. v.22 On certain arithmetical functions S. Ramanujan
8. American Mathematical Monthly v.88 no.6 Abel's theorem on the lemniscate M. Rosen
9. Introduction to the Arithmetic Theory of Automorphic Forms G. Shimura
10. Advanced Topics in the Arithmetic of Elliptic Curves J. H. Silverman
11. The Arithmetic of Elliptic Curves J. H. Silverman
12. Advances in Mathematic v.7 Values of L-functions at s = 1 1. L-functions for quasratic forms H. M. Stark