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The coefficients of certain integral modular forms

Published online by Cambridge University Press:  24 October 2008

R. A. Rankin
Affiliation:
The UniversityBirmingham 15
J. M. Rushforth
Affiliation:
The UniversityBirmingham 15

Extract

The notation which we use is that of a recent paper by one of us, and we quote results from that paper as they are required. It is known (see R, Theorem 1, for example) that the vector space k of all cusp-forms f(z) of even negative dimension – k (k ≥ 12), belonging to the full modular group Γ(1), possesses a finite basis of forms

where k is defined by (2·10) of R and the coefficients possess the following properties:

for a prime p, where p is a positive integer.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1954

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References

REFERENCES

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