Congruence Properties of Ramanujan's Function T(n) (II)

Abstract

Let T(n) be Ramanujan's function defined by

Σ T(n) xⁿ = x [(I-x) (I-x⁾²)...]²⁴.

It was recently proved by me that

T(kn-I) = 0 (mod k),            (I. I)

where k = 3, 4, 6, 8, 12 or 21 and n ≥ I. The object of this paper is to find the residues of T(n) to the moduli 3, 4 and 7.