Koutsogiannis, AndreasLe, AnhMoreira, JoelRichter, Florian Karl2021-11-262021-11-262021-11-26202110.1090/proc/15185https://infoscience.epfl.ch/handle/20.500.14299/1832402004.11835Let T be a measure-preserving Zℓ-action on the probability space (X,B,μ), let q1,…,qm:R→Rℓ be vector polynomials, and let f0,…,fm∈L∞⁡(X). For any ϵ>0 and multicorrelation sequences of the form α⁡(n)=∫Xf0⋅T⌊q1⁡(n)⌋⁢f1⋯T⌊qm⁡(n)⌋⁢fmd⁢μ we show that there exists a nil- sequence ψ for which limN−M→∞⁡1N−M⁢∑n=MN−1|α⁡(n)−ψ⁡(n)|≤ϵ and limN→∞⁡1π⁡(N)⁢∑p∈P∩[1,N]|α⁡(p)−ψ⁡(p)|≤ϵ. This result simultaneously generalizes previous results of Frantzikinakis and the authors.text::journal::journal article::research article