Cyclotomie des sommes de Weil binomiales

Weil sums of the form WK,d(a)=∑x∈Kψ(xd+ax), where K is a finite field, ψ is an additive character of K, d is coprime to |K×|, and a∈K×, arise often in number theory, as well as in finite geometry, in cryptography, in the study of the correlation of sequences, and in coding theory. Here we are interested in the case where WK,d(a) takes only three distinct values as a runs through K×. Via a Galois-theoretic approach, we give several results concerning three-valued Weil sums, and, in particular, we generalize to any nonzero characteristic some results of Calderbank-McGuire-Poonen-Rubinstein, of Calderbank-McGuire and of Charpin proved in characteristic 2.