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When we pause to reflect on Ramanujan's life, we see that there were certain events that seemingly were necessary in order that Ramanujan and his mathematics be brought to posterity. One of these was V. Ramaswamy Aiyer's founding of the Indian Mathematical Society on 4 April 1907, for had he not launched the Indian Mathematical Society, then the next(More)
A new infinite product t n was introduced by S. Ramanujan on the last page of his third notebook. In this paper, we prove Ramanu-jan's assertions about t n by establishing new connections between the modular j−invariant and Ramanujan's cubic theory of elliptic functions to alternative bases. We also show that for certain integers n, tn generates the Hilbert(More)