A formula for Ramanujan’s tau function
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- by John A. Ewell
- Proc. Amer. Math. Soc. 91 (1984), 37-40
- DOI: https://doi.org/10.1090/S0002-9939-1984-0735559-9
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Abstract:
A formula for Ramanujan’s tau function $\tau$, defined by $\sum \nolimits _1^\infty {\tau (n){x^n} = } x\prod _1^\infty {(1 - {x^n})^{24}}(\left | x \right | < 1)$, 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.
Bibliographic 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