CUBIC LEVEL ANALOGUE OF RAMANUJAN'S EISENSTEIN SERIES IDENTITIES

Print ISSN: 2319-1023 | Online ISSN: 2582-5461 | Total Downloads : 79

Abstract

Let $Q_n=1+240\sum_{k=1}^{\infty} \frac{k^3q^{nk}}{1-q^{nk}}$. On page 51-53 of his lost notebook, Ramanujan recorded very interesting identities which relates $Q_1$, $Q_5$, $Q_7$ with his theta functions. In this article, we establish analogous identities with respect to $Q_1$ and $Q_3$.

Keywords and Phrases

Ramanujan's theta functions, Eisenstein series, P-Q theta function identities.

A.M.S. subject classification

11F20, 11M36.

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