Seminar in Algebraic Geometry and Number Theory

Abstract: Random multiplicative functions have received a lot of attention in
recent years as a model for the Riemann zeta function on short intervals
on the critical line. By now, we have a good understanding of their
moments and a decent idea of their extremal behaviour, i.e., almost sure
upper and lower bounds. More recently, Soundararajan and Zaman
introduced a new model that can be thought of as a simplified function
field analogue of random multiplicative functions, and they proved
moments bounds for these quantities akin to ones of Harper. In this
talk, I will discuss almost sure lower bounds for this quantity and some
of the simplifications that can be made in the proof when compared to
the random multiplicative setting. I will moreover talk about the
optimality of these bounds.