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On Eisenstein series and
Authors:Heng Huat Chan  Yao Lin Ong
Institution:National University of Singapore, Department of Mathematics, Kent Ridge, Singapore 119260, Republic of Singapore ; National Chung Cheng University, Department of Mathematics, Min-hsiung, Chiayi 621, Taiwan, Republic of China
Abstract:In this paper, we derive some new identities satisfied by the series ${\sum _{m,n=-\infty }^{\infty }q^{m^{2}+mn+2n^{2}}}$ using Ramanujan's identities for $L(q)$, $M(q)$ and $N(q)$. Our work is motivated by an attempt to develop a theory of elliptic functions to the septic base.

Keywords:Eisenstein series  modular equations  elliptic functions
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