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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A formula for Ramanujan’s tau function
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by John A. Ewell PDF
Proc. Amer. Math. Soc. 91 (1984), 37-40 Request permission

Abstract:

A formula for Ramanujan’s tau function $\tau$, defined by $\sum \nolimits _1^\infty {\tau (n){x^n} = } x\prod _1^\infty {(1 - {x^n})^{24}}(\left | x \right | < 1)$, is presented. The author then observes that some of the known congruence properties of $\tau$ are immediate consequences of this formula representation.
References
    G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 4th ed., Clarendon Press, Oxford, 1960. S. Ramanujan, Collected papers, Chelsea, New York, 1962.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 91 (1984), 37-40
  • MSC: Primary 11F11; Secondary 11A25, 11P05
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0735559-9
  • MathSciNet review: 735559