Arithmetic Study Group: Better than squareroot cancellation for multiplicative functions
7 November 2017 14:00 in CM 219
It is a standard heuristic that sums of oscillating number theoretic functions, like the Mobius function or Dirichlet characters, should exhibit squareroot cancellation as compared with trivial bounds. It is often very difficult to prove anything as strong as that, and we generally expect that if we could prove squareroot cancellation it would be the best possible bound. I will try to explain some recent results showing that, in fact, certain averages of multiplicative functions exhibit a bit more than squareroot cancellation.