Year: 2026
Type: preprint
Abstract: Recently, the author refuted several conjectures about the vanishing of multiple correlation sequences. The goal of this paper is to provide a counterpart for the conjectures of Frantzikinakis--Kuca and of Leibman. The significance of this manuscript is twofold: firstly, we provide a structure theorem for multiple correlation sequences on nilsystems along arithmetic progressions (in the sense of Frantzikinakis--Kuca), and a corresponding structure theorem for polynomial orbits of subnilmanifolds in connected nilmanifolds (in the sense of Leibman). Secondly, we identify null generalized nilsequences, as a notion of smallness, which provides a structured counterpart for null sequences. In particular, in the special case of ergodic nilsystems, we answer positively a question of Frantzikinakis on the structure of multiple correlation sequences.
Source: arXiv (Cornell University)
Author: Shalom, Or
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224025631