The l^1-norm of the Fourier transform on compact vector spaces
arXiv:math/0605519 · doi:10.1112/blms/bdm010
Abstract
Suppose that A is a subset of F_2^n of density as close to 1/3 as possible. We show that the A(F_2^n)-norm (that is the sum of the absolute values of the Fourier transform) of the characterstic function of A is bounded below by an absolute constant times log n as n tends to infinity.
13 pp. Corrected typos. Updated references.