Structured extensions and multi-correlation sequences
Dynamical Systems
2025-11-18 v2 Number Theory
Abstract
We show that every multi-correlation sequence is the sum of a generalized nilsequence and a null-sequence. This proves a conjecture of N. Frantzikinakis. A key ingredient is the reduction of ergodic multidimensional inverse theorems to analogous finitary inverse theorems, offering a new approach to the structure theory of multidimensional Host-Kra factors. This reduction is proven by combining the methods of Tao (2015) with the Furstenberg correspondence principle. We also prove the analogous multidimensional finitary inverse theorem with quasi-polynomial bounds.
Cite
@article{arxiv.2504.07038,
title = {Structured extensions and multi-correlation sequences},
author = {James Leng},
journal= {arXiv preprint arXiv:2504.07038},
year = {2025}
}
Comments
61 pages, added Appendix C and remark 1.7, changes to Lemma 6.2. arXiv admin note: text overlap with arXiv:2402.17994