Multiple ergodic averages for variable polynomials

Abstract

<p style='text-indent:20px;'>In this paper we study multiple ergodic averages for "good" variable polynomials. In particular, under an additional assumption, we show that these averages converge to the expected limit, making progress related to an open problem posted by Frantzikinakis ([<xref ref-type="bibr" rid="b13">13</xref>,Problem 10]). These general convergence results imply several variable extensions of classical recurrence, combinatorial and number theoretical results which are presented as well.</p>