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.References
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Additional Information
- Heng Huat Chan
- Affiliation: National University of Singapore, Department of Mathematics, Kent Ridge, Singapore 119260, Republic of Singapore
- MR Author ID: 365568
- Email: chanhh@math.nus.sg
- Yao Lin Ong
- Affiliation: National Chung Cheng University, Department of Mathematics, Min-hsiung, Chiayi 621, Taiwan, Republic of China
- Email: d8521002@willow.math.ccu.edu.tw
- Received by editor(s): September 11, 1997
- Published electronically: February 11, 1999
- Communicated by: David E. Rohrlich
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1735-1744
- MSC (1991): Primary 33E05, 11Y60
- DOI: https://doi.org/10.1090/S0002-9939-99-04832-7
- MathSciNet review: 1600120