Ideals Generated by Exponential-Polynomials

In several problems in Harmonic Analysis, .and in Number Theory as well, lemmas on small values of holomorphic functions play an important role. Let us give first an example from Harmonic Analysis. distributions with compact support in 17% " whose Fourier transforms satisfy, in C " , a lower estimate of the form (0.2) with v, ,..., v, also distributions with compact support 131, 33). In many examples (0.1) cannot be verified, even if one knows that the functions @I have no common zeroes in C " , without recourse to deep results in number theory (see, e.g., .[12]). On the other hand, using again examples of a number theoretical nature one can find simple examples showing