On Benford's Law for multiplicative functions
Number Theory
2022-04-04 v2
Abstract
We provide a criterion to determine whether a real multiplicative function is a strong Benford sequence. The criterion implies that the -divisor functions, where , and Hecke eigenvalues of newforms, such as Ramanujan tau function, are strong Benford. Moreover, we deduce from the criterion that the collection of multiplicative functions which are not strong Benford forms a group under pointwise multiplication. In contrast to earlier work, our approach is based on Hal\'{a}sz's Theorem.
Keywords
Cite
@article{arxiv.2203.13117,
title = {On Benford's Law for multiplicative functions},
author = {Vorrapan Chandee and Xiannan Li and Paul Pollack and Akash Singha Roy},
journal= {arXiv preprint arXiv:2203.13117},
year = {2022}
}
Comments
12 pages; new version with two new coauthors, updates to main theorem and added Corollary 1.7