# Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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## Structure of multicorrelation sequences with integer part polynomial iterates along primesHTML articles powered by AMS MathViewer

by Andreas Koutsogiannis, Anh N. Le, Joel Moreira and Florian K. Richter
Proc. Amer. Math. Soc. 149 (2021), 209-216 Request permission

## Abstract:

Let $T$ be a measure-preserving $\mathbb {Z}^\ell$-action on the probability space $(X,{\mathcal B},\mu ),$ let $q_1,\dots ,q_m\colon \mathbb {R}\to \mathbb {R}^\ell$ be vector polynomials, and let $f_0,\dots ,f_m \in L^\infty (X)$. For any $\epsilon > 0$ and multicorrelation sequences of the form $\alpha (n) =\int _Xf_0\cdot T^{ \lfloor q_1(n) \rfloor }f_1\cdots T^{ \lfloor q_m(n) \rfloor }f_m\;d\mu$ we show that there exists a nil- sequence $\psi$ for which $\lim _{N - M \to \infty } \frac {1}{N-M} \sum _{n=M}^{N-1} |\alpha (n) - \psi (n)| \leq \epsilon$ and $\lim _{N \to \infty } \frac {1}{\pi (N)} \sum _{p \in \mathbb {P}\cap [1,N]} |\alpha (p) - \psi (p)| \leq \epsilon .$ This result simultaneously generalizes previous results of Frantzikinakis and the authors.
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• Andreas Koutsogiannis
• Affiliation: Department of Mathematics, The Ohio State University, Columbus, Ohio
• MR Author ID: 974679
• Email: koutsogiannis.1@osu.edu
• Anh N. Le
• Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois
• ORCID: 0000-0003-4928-4932
• Email: anhle@math.northwestern.edu
• Joel Moreira
• Affiliation: Mathematics Institute, University of Warwick, Coventry, United Kingdom
• MR Author ID: 1091663
• Email: joel.moreira@warwick.ac.uk
• Florian K. Richter
• Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois
• MR Author ID: 1147216
• Email: fkr@northwestern.edu
• Received by editor(s): April 24, 2020
• Published electronically: October 16, 2020
• Additional Notes: The fourth author was supported by the National Science Foundation under grant number DMS 1901453.
• Communicated by: Katrin Gelfert