On a paper of Dressler and Van de Lune

Abstract

If z∈ C and 1 ≤ n is a natural number then ∑d1d2=n(1-zp1)⋯(1-zpm)zq1e1+⋯+qiei=1, where d1=p1r1⋯pmrm, d2=q1e1⋯qiei are the prime decompositions of d1, d2. This is one of the identities involving arithmetic functions that we prove using ideas from the paper of Dressler and van de Lune [3].