Le poids des polynomes irreductibles a coefficients dans un corps fini

This work concerns the weight of irreducible polynomials over a finite field, i.e., the number of non-zero coefficients of these polynomials. We introduce a polynomial analog of the Vinogradov's method developed by Gallagher and Vaughan, which leads to upper bounds for associated exponential sums. This allows us to study the distribution of the weight of irreducible polynomials in arithmetic progressions and to provide an asymptotic estimate (with an error term) for the number of irreducible polynomials of given degree whose weight is close to the expected value.