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Multiple ergodic averages for commuting multiplicative actions
We study the convergence of multiple ergodic averages involving several commuting multiplicative actions. We prove that for finitely generated systems, the averages $$\frac{1}{N}\sum_{n=1}^N S_{1,n}F_1\cdot\ldots\cdot S_{\ell,n}F_\ell$$ converge in norm, settling a conjecture of Frantzikinakis. Ou
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