Hostname: page-component-8448b6f56d-gtxcr Total loading time: 0 Render date: 2024-04-24T23:20:21.475Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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