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

Abstract

In this and the succeeding paper I solve two problems suggested by Prof. Hardy, namely (1) that of proving that Ramanujan's functionhas no zeros on the line and (2) that of finding an asymptotic formulawhere A is a constant. I also prove similar results concerning the coefficients of general modular forms. I am indebted to Prof. Hardy and Mr Ingham for various suggestions, and in particular to Mr Ingham's paper, “A note on Riemann's ζ-function and Dirichlet's L-functions”.