A Correspondence Principle for the Gowers Norms

TL;DR

This paper introduces a variation of the Furstenberg Correspondence that maintains the Gowers uniformity norms, providing a new tool for analyzing uniformity in additive combinatorics.

Contribution

It presents a novel correspondence principle that preserves Gowers norms, bridging combinatorial and ergodic theoretical approaches.

Findings

Preserves Gowers uniformity norms in the correspondence

Enables new analysis techniques in additive combinatorics

Bridges combinatorial and ergodic methods

Abstract

We give a variation of the Furstenberg Correspondence which preserves the Gowers uniformity norms.