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- W4287183782 abstract "A recent result of Frantzikinakis establishes sufficient conditions for joint ergodicity in the setting of $mathbb{Z}$-actions. We generalize this result for actions of second-countable locally compact abelian groups. We obtain two applications of this result. First, we show that, given an ergodic action $(T_n)_{n in F}$ of a countable field $F$ with characteristic zero on a probability space $(X,mathcal{B},mu)$ and a family ${p_1,dots,p_k}$ of independent polynomials, we have [ lim_{N to infty} frac{1}{|Phi_N|}sum_{n in Phi_N} T_{p_1(n)}f_1cdots T_{p_k(n)}f_k = prod_{j=1}^k int_X f_i dmu,] where $f_i in L^{infty}(mu)$, $(Phi_N)$ is a F{o} lner sequence of $(F,+)$, and the convergence takes place in $L^2(mu)$. This yields corollaries in combinatorics and topological dynamics. Second, we prove that a similar result holds for totally ergodic actions of suitable rings." @default.
- W4287183782 created "2022-07-25" @default.
- W4287183782 creator A5021514058 @default.
- W4287183782 creator A5026910147 @default.
- W4287183782 date "2021-05-09" @default.
- W4287183782 modified "2023-10-18" @default.
- W4287183782 title "Polynomial ergodic averages for certain countable ring actions" @default.
- W4287183782 doi "https://doi.org/10.48550/arxiv.2105.04008" @default.
- W4287183782 hasPublicationYear "2021" @default.
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