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Schlafli-type Mixed Modular Equations of Degrees 1, 3, n, and 3n

Volume 18, Number 1 (2015), 55 - 76

Schlafli-type Mixed Modular Equations of Degrees 1, 3, n, and 3n

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Abstract

In this paper, we establish several new Schl\"{a}fli-type mixed modular equations of composite degrees. These equations are analogous to those recorded by Ramanujan in his second notebook. As an application, we establish several new explicit values for the Ramanujan-Weber class invariant $G_{n}$ for $n=12, 48, 51, 57, 3/4, 3/16, 3/17$ and $3/19$.