Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Structure of multicorrelation sequences with integer part polynomial iterates along primes


Authors: Andreas Koutsogiannis, Anh N. Le, Joel Moreira and Florian K. Richter
Journal: Proc. Amer. Math. Soc. 149 (2021), 209-216
MSC (2010): Primary 37A45, 37A15; Secondary 11B30
DOI: https://doi.org/10.1090/proc/15185
Published electronically: October 16, 2020
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 \linebreak\in L^\infty (X)$. For any $ \epsilon > 0$ and multicorrelation sequences of the form $ \alpha (n) \linebreak =\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} \vert\alpha (n) - \psi (n)\vert \leq \epsilon $ and
$ \lim _{N \to \infty } \frac {1}{\pi (N)} \sum _{p \in \mathbb{P}\cap [1,N]} \vert\alpha (p) - \psi (p)\vert \leq \epsilon .$ This result simultaneously generalizes previous results of Frantzikinakis and the authors.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 37A45, 37A15, 11B30

Retrieve articles in all journals with MSC (2010): 37A45, 37A15, 11B30


Additional Information

Andreas Koutsogiannis
Affiliation: Department of Mathematics, The Ohio State University, Columbus, Ohio
Email: koutsogiannis.1@osu.edu

Anh N. Le
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois
Email: anhle@math.northwestern.edu

Joel Moreira
Affiliation: Mathematics Institute, University of Warwick, Coventry, United Kingdom
Email: joel.moreira@warwick.ac.uk

Florian K. Richter
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois
Email: fkr@northwestern.edu

DOI: https://doi.org/10.1090/proc/15185
Keywords: Multicorrelation sequences, nilsequences, integer part polynomials, prime numbers
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
Article copyright: © Copyright 2020 American Mathematical Society