On Eisenstein series and ∑_{𝑚,𝑛=-∞}^{∞}𝑞^{𝑚²+𝑚𝑛+2𝑛²}

Chan, Heng Huat; Ong, Yao

doi:10.1090/S0002-9939-99-04832-7

On Eisenstein series and $\sum _{m,n=-\infty }^{\infty } q^{m^2+mn+2n^2}$
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by Heng Huat Chan and Yao Lin Ong PDF

Proc. Amer. Math. Soc. 127 (1999), 1735-1744 Request permission

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.

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