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On the order of magnitude of Ramanujan's arithmetical function τ(n)

Published online by Cambridge University Press:  24 October 2008

W. B. Pennington
W. B. Pennington
Affiliation:
Harvard University
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Extract

1. In his paper ‘On certain arithmetical functions' Ramanujan (23) considers the function τ(n) defined by the expansion

This function appears in the discussion of an asymptotic formula for the function

and also in Ramanujan's formula for the number of representations of an integer as the sum of 24 squares. It is also of interest as the coefficient in the expansion of g(z), which plays an important part in the theory of modular functions.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 4 , October 1951 , pp. 668 - 678
Copyright
Copyright © Cambridge Philosophical Society 1951

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References

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