This week's seminars
Arithmetic Study Group: Lacunary discrete spherical averages
15 October 2019 13:00 in CM219
We will discuss an arithmetic version of Stein's spherical averages. Their associated full maximal function was studied by Magyar--Stein--Wainger and Ionescu who gave the sharp range of estimates. Magyar subsequently proved that the associated ergodic averages converge almost everywhere. In analogy with Stein's spherical averages, one would expect the lacunary averages to have much better behavior. We will show that to some extent they do, but with surprising limitations.