Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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
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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.

Keywords

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