A family of Eta Quotients and an Extension of the Ramanujan-Mordell Theorem

Ayse Alaca; Saban Alaca; Zafer Selcuk Aygin

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arXiv · 1603.09412

A family of Eta Quotients and an Extension of the Ramanujan-Mordell Theorem

Ayse Alaca·Saban Alaca·Zafer Selcuk Aygin

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Abstract

Let $k\geq 2$ be an integer and $j$ an integer satisfying $1\leq j \leq 4k-5$. We define a family $\{ C_{j,k}(z) \}_{1\leq j \leq 4k-5} $ of eta quotients, and prove that this family constitute a basis for the space $S_{2k} (\Gamma_0 (12))$ of cusp forms of weight $2k$ and level $12$. We then use this basis together with certain properties of modular forms at their cusps to prove an extension of the Ramanujan-Mordell formula.

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Ayse Alaca, Saban Alaca, Zafer Selcuk Aygin. 2016-03-30. A family of Eta Quotients and an Extension of the Ramanujan-Mordell Theorem. https://arxiv.org/abs/1603.09412

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