On Benford’s law for multiplicative functions

Abstract

We provide a criterion to determine whether a real multiplicative function is a strong Benford sequence. The criterion implies that the k k -divisor functions, where k ≠ 10 j k \neq 10^j , and Hecke eigenvalues of newforms, such as Ramanujan tau function, are strong Benford. In contrast to some earlier work, our approach is based on Halász’s Theorem.