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Multiple recurrence and convergence results associated to \({\text{F}}_P^\omega \)-actions

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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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Author information

Authors and Affiliations

  1. Department of Mathematics, The Ohio-State University, Columbus, OH, 43210, USA

    Vitaly Bergelson

  2. Department of Mathematics, UCLA, Los Angeles, CA, 90095-1555, USA

    Terence Tao

  3. Department of Mathematics Technion, Haifa, Israel, 32000

    Tamar Ziegler

Authors
  1. Vitaly Bergelson
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  2. Terence Tao
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  3. Tamar Ziegler
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Corresponding author

Correspondence to Vitaly Bergelson.

Additional information

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

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