Nonconventional ergodic averages and nilmanifolds
Nonconventional ergodic averages and nilmanifolds
We study the L 2 -convergence of two types of ergodic averages.The first is the average of a product of functions evaluated at return times along arithmetic progressions, such as the expressions appearing in Furstenberg's proof of Szemerédi's theorem.The second average is taken along cubes whose sizes tend to +∞.For …