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A further note on Ramanujan's arithmetical function τ(n)

Published online by Cambridge University Press:  24 October 2008

G. H. Hardy
G. H. Hardy
Affiliation:
Trinity College
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Extract

This note is a sequel to two in earlier volumes of the Proceedings, the first by myself and the second by Wilton†.

Suppose that

for |z| <1; that x > 0; that

forr ≥ 0; and that

where τ(x) is to mean 0 if x is not an integer. Thus

where the dash shows that the last term is to be halved when x is an integer;

forr > 1; and

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 34 , Issue 3 , July 1938 , pp. 309 - 315
Copyright
Copyright © Cambridge Philosophical Society 1938

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References

REFERENCES

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