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

 

A formula for Ramanujan's tau function


Author: John A. Ewell
Journal: Proc. Amer. Math. Soc. 91 (1984), 37-40
MSC: Primary 11F11; Secondary 11A25, 11P05
MathSciNet review: 735559
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Abstract: A formula for Ramanujan's tau function $ \tau $, defined by $ \sum\nolimits_1^\infty {\tau (n){x^n} = } x\prod _1^\infty {(1 - {x^n})^{24}}(\left\vert x \right\vert < 1)$, is presented. The author then observes that some of the known congruence properties of $ \tau $ are immediate consequences of this formula representation.


References [Enhancements On Off] (What's this?)

  • [1] G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 4th ed., Clarendon Press, Oxford, 1960.
  • [2] S. Ramanujan, Collected papers, Chelsea, New York, 1962.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0735559-9
PII: S 0002-9939(1984)0735559-9
Keywords: Ramanujan's tau function
Article copyright: © Copyright 1984 American Mathematical Society