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CERTAIN RATIONAL FUNCTION OF SINGULAR MODULI FOUND IN RAMANUJAN'S FIRST NOTEBOOK
M. S. M. Naikai,C. Shivashankar,M. Harish 장전수학회 2015 Advanced Studies in Contemporary Mathematics Vol.25 No.1
On page 312 in his rst notebook, Ramanujan denes a certain rational function of singular moduli Un and records 11 explicit values of Un. All these values have been proved by using the known values of the class invariant gn. In this paper, we establish modular relation between certain rational function of singular moduli Un and Uk2n for k = 2; 3; 5; 7; 9 and 11. As an application, we also establish several new values of Un.