Abstract
This project has two main objectives: the first is to determine the number of rational points of Artin-Schreier hypersurfaces, which are hypersurfaces of the form y^q-y=f(X), with f(X) \in F_q[X]{0} and X=(x_1,...,x_r), imposing some conditions on f. This problem has already been partially studied in my Ph.D thesis in the case where f is a sum of binomials of the form a_j x_j(x_j^{q^{i_j}…