On Ramanujan's Quartic Theory of Elliptic Functions
by
Wen-Chin Liaw
National Chung Cheng University
Coauthors: Bruce C. Berndt (University of Illinois at Urbana-Champaign)

In 1995, B.~C. Berndt, S. Bhargava, and F.~G. Garvan developed in greater detail the theories of elliptic functions of signature 3, 4, and 6 than those only vaguely mentioned by Ramanujan. In particular, they derived the theory of signature 4 from the classical theory by a transfer principle between these two theories. In this paper, instead of relying on the transfer principle, we take a direct approach to the quartic theory in the same spirit of its classical and cubic counterparts.

http://lilac.math.ccu.edu.tw/~wcliaw/

Date received: March 15, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caew-09.