Random multiplicative functions f(n)f(n) are a well studied random model for deterministic multiplicative functions like Dirichlet characters or the Mobius function. Arguably the first question ever studied about them, by Wintner in 1944, was to obtain almost sure bounds for the largest fluctuations of their partial ∑n≤xf(n)∑n≤xf(n), seeking to emulate the classical Law of the Iterated Logarithm for independent random variables. It remains an open question to sharply determine the size of these fluctuations, and in this talk I will describe a new result in that direction. I hope to get to some interesting details of the new proof in the latter part of the talk, but most of the discussion should be widely accessible.

This talk is part of the online Number Theory Web Seminar, and will be streamed live on Zoom.

To attend the talks, registration is necessary. To register please visit our website


Registered users will receive an email before each talk with a link to the Zoom meeting.


Mike Bennett (University of British Columbia)

Philipp Habegger (University of Basel)

Alina Ostafe (UNSW Sydney)


Adam Harper

Research Area

Number Theory Seminar


University of Warwick


Tue, 15/12/2020 - 9:00pm


RC-4082, The Red Centre, UNSW