On Benford's law for multiplicative functions

Abstract: Benford's law is a phenomenon about the first digits of the numbers in data sets. In particular, the leading digits does not exhibit uniform distribution as might be naively expected, but rather, the digit appears the most, followed by , and so on until . In this talk, I will discuss my recent joint work with Xiannan Li, Paul Pollack and Akash Sigha Roy on a criterion to determine whether a real multiplicative function is a Benford sequence. The criterion implies that the divisor functions and Hecke eigenvalues of newforms, such as Ramanujan tau function, are Benford. In contrast to earlier work, our approach is based on Halasz's Theorem.

number theory

Audience: researchers in the topic

Around Frobenius Distributions and Related Topics IV

Series comments: Registration is free, but all participants are required to register on the conference website.