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Contributions to the theory of Ramanujan's function τ(n) and similar arithmetical functions

iii. a note on the sum function of the fourier coefficients of integral modular forms

Published online by Cambridge University Press:  24 October 2008

R. A. Rankin
R. A. Rankin
Affiliation:
Clare CollegeCambridge
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Extract

Suppose that is an integral modular form of dimensions − κ, where κ > 0, and Stufe N, which vanishes at all the rational cusps of the fundamental region, and which is absolutely convergent for The purpose of this note is to prove that

The notation employed is that of my second paper under the same general title* I refer to this paper as II.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 36 , Issue 2 , April 1940 , pp. 150 - 151
Copyright
Copyright © Cambridge Philosophical Society 1940

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References

REFERENCES

(1)Rankin, R. A. “Contributions to the theory of Ramanujan's function τ(n). II. The order of the Fourier coefficients of integral modular forms.” Proc. Cambridge Phil. Soc. 35 (1939), 357–72.CrossRefGoogle Scholar
(2)Walfisz, A. “Koeffizientensummen einiger Modulformen.” Math. Annalen, 108 (1933), 75–90.CrossRefGoogle Scholar
(3)Hardy, G. H. “A further note on Ramanujan's arithmetical function τ(n).” Proc. Cambridge Phil. Soc. 34 (1938), 309–15.CrossRefGoogle Scholar