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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On Eisenstein series and $\sum _{m,n=-\infty }^{\infty }q^{m^{2}+mn+2n^{2}}$


Authors: Heng Huat Chan and Yao Lin Ong
Journal: Proc. Amer. Math. Soc. 127 (1999), 1735-1744
MSC (1991): Primary 33E05, 11Y60
Published electronically: February 11, 1999
MathSciNet review: 1600120
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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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Additional Information

Heng Huat Chan
Affiliation: National University of Singapore, Department of Mathematics, Kent Ridge, Singapore 119260, Republic of Singapore
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

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04832-7
PII: S 0002-9939(99)04832-7
Keywords: Eisenstein series, modular equations, elliptic functions
Received by editor(s): September 11, 1997
Published electronically: February 11, 1999
Communicated by: David E. Rohrlich
Article copyright: © Copyright 1999 American Mathematical Society