A short proof of Helson's conjecture
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.
Authors
- Mo Dick Wong (ORCID: https://orcid.org/0000-0003-0592-4715)
- Ofir Gorodetsky (ORCID: https://orcid.org/0000-0002-1435-9650)
Institutions
- Technion – Israel Institute of Technology (IL)
- Durham University (GB)
Publication Details
- Journal
- Bulletin of the London Mathematical Society
- Published
- 2025-02-07
- DOI
- https://doi.org/10.1112/blms.70015
- Citations
- 1
- Primary Topic
- Mathematics and Applications
- Type
- article
- Field-Weighted Citation Impact
- 4.09
Funders
- European Research Council