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arXiv · 2504.07038

Structured extensions and multi-correlation sequences

James Leng
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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.

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James Leng. 2025-04-09. Structured extensions and multi-correlation sequences. https://arxiv.org/abs/2504.07038

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