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

 

New representations of Ramanujan's tau function


Author: John A. Ewell
Journal: Proc. Amer. Math. Soc. 128 (2000), 723-726
MSC (1991): Primary 11A25; Secondary 11B75
Published electronically: July 28, 1999
MathSciNet review: 1657735
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Abstract: Several formulas for Ramanujan's function $\tau$, defined by

\begin{displaymath}x \prod _1^{\infty}(1-x^n)^{24}=\displaystyle\sum _1^{\infty} \tau (n) x^n \quad (\vert x \vert < 1), \end{displaymath}

are presented. We also present a congruence modulo 3 for some of the function values.


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Additional Information

John A. Ewell
Affiliation: Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05289-2
PII: S 0002-9939(99)05289-2
Keywords: Ramanujan's tau function
Received by editor(s): May 13, 1998
Published electronically: July 28, 1999
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 1999 American Mathematical Society