English

The Littlewood-Gowers problem

Classical Analysis and ODEs 2010-04-02 v2 Combinatorics

Abstract

We show that if A is a subset of Z/pZ (p a prime) of density bounded away from 0 and 1 then the A(Z/pZ)-norm (that is the l^1-norm of the Fourier transform) of the characterstic function of A is bounded below by an absolute constant times (log p)^{1/2 - \epsilon} as p tends to infinity. This improves on the exponent 1/3 in recent work of Green and Konyagin.

Keywords

Cite

@article{arxiv.math/0605522,
  title  = {The Littlewood-Gowers problem},
  author = {Tom Sanders},
  journal= {arXiv preprint arXiv:math/0605522},
  year   = {2010}
}

Comments

31 pp. Corrected typos. Updated references.

R2 v1 2026-07-22T17:36:10.401Z