Work

A short proof of Helson's conjecture

Year: 2025

Type: article

Abstract: Let be the Steinhaus multiplicative function: a completely multiplicative function such that are i.i.d. random variables uniformly distributed on the complex unit circle . Helson conjectured that as , and this was solved in a strong form by Harper. We give a short proof of the conjecture using a result of Saksman and Webb on a random model for the zeta function.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70015

Authors: Ofir Gorodetsky, Mo Dick Wong

Institutions: Technion – Israel Institute of Technology, Durham University

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: European Commission, European Research Council, H2020 European Research Council