Abstract
Using an ergodic inverse theorem obtained in our previous paper, we obtain limit formulae for multiple ergodic averages associated with the action of \({\text{F}}_p^\omega = \oplus {{\text{F}}_p}\). From this we deduce multiple Khintchine-type recurrence results analogous to those for ℤ-systems obtained by Bergelson, Host, and Kra, and also present some new counterexamples in this setting.
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The first author is supported by support NSF grant DMS-1162073.
The second author is supported by NSF grant DMS-0649473 and by a Simons Investigator Award.
The third author is supported by ISF grant 407/12.
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Bergelson, V., Tao, T. & Ziegler, T. Multiple recurrence and convergence results associated to \({\text{F}}_P^\omega \)-actions. JAMA 127, 329–378 (2015). https://doi.org/10.1007/s11854-015-0033-1
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DOI: https://doi.org/10.1007/s11854-015-0033-1