is it true that If(s) I_k>0 for o 0 implies that (f(s))-l is also of the form (1)? In this note, an affirmative answer is supplied.3 Let P be the semigroup of positive integers under multiplication, and let l1(P) be the class of all complex functions a on P, a = { an},1 for which aIlal = I:| an| is finite. We obtain a commutative Banach algebra by defining (aa)n= aan for complex a, (a+b)n=a.+bn, and the product a * b (convolution) by (a * b)n = Zjkn ajbk. The algebra l1(P) has as its unit e the function such that el =1 and en = 0 if n> 1. The theory of l1-algebras of commutative semigroups is developed in [4] and [5]. The present note is based on the observation that the Dirichlet series (1) is the Fourier transform of the element aell(P), defined on a very small subspace of the space of all maxi al ideals of l1(P).