A Note on Dirichlet Convolutions

Abstract

In [3] Rubel proved that if h(n) is an arithmetic function such that , L finite, then where μ(n) is the Mobius function. This result was extended to functions other than μ(n) in [4]; however, (as first pointed out to the author by Benjamin Volk), the order condition imposed there is unnecessary; in fact, utilizing the result of [3], the following slightly more general theorem has an almost trivial proof.