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Ramanujan's Singular Moduli |
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| Authors: | Berndt Bruce C. Chan Heng Huat Zhang Liang-Cheng |
| Affiliation: | (1) Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois, 61801;(2) School of Mathematics, Institute for Advanced Study, Princeton, New Jersey, 08540;(3) Department of Mathematics, Southwest Missouri State University, Springfield, Missouri, 65804 |
| 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 |
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