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Cubic singular
moduli, Ramanujan’s class invariants λn
and the explicit Shimura Reciprocity Law
Heng Huat Chan, Victor Tan and Alice Gee |
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Vol. 208 (2003), No. 1, 23–37
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Abstract |
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In this paper, we use the explicit Shimura Reciprocity Law to compute the cubic singular moduli αn∗, which are used in the constructions of new rapidly convergent series for 1∕π. We also complete a table of values for the class invariant λn initiated by S. Ramanujan on page 212 of his Lost Notebook. |
Milestones
Received: 13 April 2001
Revised: 7 November 2001
Published: 1 January 2003
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Authors |
| Heng Huat Chan | |
| Department of Mathematics National University of Singapore Kent Ridge, Singapore 119260 Republic of Singapore |
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| Victor Tan | |
| Department of Mathematics National University of Singapore Kent Ridge, Singapore 119260 Republic of Singapore |
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| Alice Gee | |
| Department of Mathematics University of Amsterdam The Netherlands |
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