BRUCE C. BERNDT
Department of Mathematics, University of
Illinois, Urbana, Illinois 61801
berndt@math.uiuc.edu
HENG HUAT CHAN
School of Mathematics, Institute for Advanced Study, Princeton,
New Jersey 08540
hhchan@math.ccu.edu.tw
LIANG-CHENG ZHANG
Department of Mathematics, Southwest Missouri State University, Springfield,
Missouri 65804
liz917f@smsuma.bitnet
Received August 30, 1995; Accepted April 8, 1996
Abstract. In his first notebook, in scattered places, Ramanujan recorded without proofs the values of over 100 class invariants and over 30 singular moduli. This paper is devoted to establishing all of Ramanujan's representations for singular moduli. For those of odd index, new algorithms needed to be developed.
Keywords: Ramanujan-Weber class invariants, singular moduli, modular equations, theta-functions
1991 Mathematics Classification: Primary - 11F20; Secondary - 33D10, 33E05