A nilpotent IP polynomial multiple recurrence theorem

Abstract

We generalize the IP-polynomial Szemerédi theorem due to Bergelson and McCutcheon and the nilpotent Szemerédi theorem due to Leibman. Important tools in our proof include a generalization of Leibman's result that polynomial mappings into a nilpotent group form a group and a multiparameter version of the nilpotent Hales-Jewett theorem due to Bergelson and Leibman.

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Cited by in corpus (5)

• Norm convergence of multiple ergodic averages on amenable groups
• Ergodic theorems for polynomials in nilpotent groups
• Topological correspondence of multiple ergodic averages of nilpotent group actions
• Combinatorial properties of Nil-Bohr sets
• Applications of Ultrafilters in Ergodic Theory and Combinatorial Number Theory