Abstract

Let f be a function transcendental and meromorphic in the plane with

	lim inf	T(r, f)/(log r)2		=0.
	r → ∞

Let q = ࠶ with |q| > 1. It is shown that at least one of the functions

F(z) = f(qz) -f(z), G(z)= F(z)/f(z)

has infinitely many zeros. This result is sharp.