Nonconventional ergodic averages and nilmanifolds

@article{Host2005NonconventionalEA,
  title={Nonconventional ergodic averages and nilmanifolds},
  author={Bernard Host and Bryna Kra},
  journal={Annals of Mathematics},
  year={2005},
  volume={161},
  pages={397-488}
}
We study the L2-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?fs proof of Szemer?Ledi?fs theorem. The second average is taken along cubes whose sizes tend to +??. For each average, we show that it is sufficient to prove the convergence for special systems, the characteristic factors. We build these factors in a general way, independent of… 

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