Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

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

II. The order of the Fourier coefficients of integral modular forms

R. A. Rankina1

a1 Clare College Cambridge

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 S0305004100021101_inline1 Then


where a, b, c, d are integers such that ad − bc = 1.

(Received April 17 1939)