Estimating the first zero of a characteristic function

For a characteristic function (Fourier transform of a probability distribution), the first zero encodes important information. We present a general lower bound estimation of the first zero in terms of a moment of any order. The result proves the complementary nature between the first zero and moments, and has interesting implications for quantum mechanical uncertainty relations. (C) 2003 Academie des sciences. Published by Elsevier SAS. All rights reserved.