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Vietnam Journal of Mathematics 36:2(2008) 103-124

On Some New Explicit Evaluations of Class Invariants 

M. S. Mahadeva Naika and K. Sushan Bairy

Abstract.  Ramanujan recorded the values for 107 class invariants or polynomials satisfied by them at scattered places of his first notebook. On pages 294-299 in his second notebook, Ramanujan gave a table of values for 77 class invariants. In this paper, we establish some connecting formulas for G_n and g_n. We also establish several new explicit evaluations of Ramanujan-Weber type class invariants using the modular equations and several explicit values of singular moduli.

2000 Mathematics Subject Classification: 33D10, 11F27.

Keywords: Modular equation, Theta-function, class invariant, singular moduli.

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Published by Springer since January 2013