The Littlewood-Gowers problem

Details The Littlewood-Gowers problem The Littlewood-Gowers problem

2006-05-18

arxiv.org/abs/math/0605522v2

J. Anal. Math. 101 (2007), 123-162

Mathematics

Classical Analysis and ODEs

31 pp. Corrected typos. Updated references.

Scientific paper

10.1007/s11854-007-0005-1

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.

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