Better than squareroot cancellation in number theory
Abstract
We give a short survey of the phenomenon of better than squareroot cancellation, specifically as it applies to averages of multiplicative character sums (such as 1r-1 Σ \; mod \; r |Σn ≤ x (n)|2q) thanks to their connection with so-called multiplicative chaos. We focus on the number theoretic aspects of the arguments, and also touch on some possible applications.
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