The Inverse Conjecture for The Gowers Norm Over Finite Fields Via The Correspondence Principle

Terence Tao*, Tamar Ziegler

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

43 Scopus citations

Abstract

The inverse conjecture for the Gowers norms Ud(V) for finite-dimensional vector spaces V over a finite field F asserts, roughly speaking, that a bounded function f has large Gowers norm ∥ f ∥Ud(V)if and only if it correlates with a phase polynomial (Equation Presented) of degree at most d-1, thus P:V ⌜ F is a polynomial of degree at most d-1. In this paper, we develop a variant of the Furstenberg correspondence principle which allows us to establish this conjecture in the large characteristic case char F > d from an ergodic theory counterpart, which was recently established by Bergelson, Tao and Ziegler.

Original languageAmerican English
JournalAnalysis and PDE
Volume3
Issue number1
DOIs
StatePublished - 2010
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2010 by Mathematical Sciences Publishers

Keywords

  • Characteristic factor
  • Furstenberg correspondence principle
  • Gowers uniformity norm
  • Polynomials over finite fields

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