The Littlewood-Gowers problem

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 - ε} as p tends to infinity. This improves on the exponent 1/3 in recent work of Green and Konyagin.

31 pp. Corrected typos. Updated references.

References in corpus (3)

• Additive structures in sumsets
• An inverse theorem for the Gowers U^3 norm
• The l^1-norm of the Fourier transform on compact vector spaces

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• Dependent Random Choice
• The largest $(k,\ell )$-sum-free subsets
• Lower bounds for the Wiener norm in ${\mathbb{Z}}_p^d$