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Some open problems on multiple ergodic averages. (English) Zbl 1425.37004

Summary: We survey some recent developments and give a list of open problems regarding multiple recurrence and convergence phenomena of \(\mathbb{Z}^d\) actions in ergodic theory and related applications in combinatorics and number theory.

MSC:

37A30 Ergodic theorems, spectral theory, Markov operators
05D10 Ramsey theory
11B30 Arithmetic combinatorics; higher degree uniformity
11N37 Asymptotic results on arithmetic functions
37A45 Relations of ergodic theory with number theory and harmonic analysis (MSC2010)
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References:

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