Ergodic theorems for polynomials in nilpotent groups

2013/09/02 by Pavel Zorin‐Kranich, Pavel Zorin-Kranich, Zorin-Kranich, Pavel
Mathematics · #37A30 #Dynamical Systems (math.DS) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Limits and Structures in Graph Theory #math.DS #msc:37A30

paper · pdf · doi:10.48550/arxiv.1309.0345

PhD thesis, University of Amsterdam, xi+146 pages. Based on arXiv:1111.7292, arXiv:1206.0287, arXiv:1208.3977, arXiv:1210.5202, arXiv:1301.1884

arxiv created 2013/09/02 · openalex publication_date 2013/09/02 · arxiv updated 2013/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The principal results proved in this expository thesis are the IP polynomial Szemerédi theorem for nilpotent groups and the multiple term return times theorem with nilsequence weights. It also contains extensions of the convergence theorem for nilpotent polynomial multiple ergodic averages and the return times theorem to locally compact second countable amenable groups.

Citations

• Nilspaces, nilmanifolds and their morphisms
• On the speed of convergence in the ergodic theorem
• Uniformity in the Wiener-Wintner theorem for nilsequences

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