Histoires de formes trilinéaires et de vecteurs test

Louise Nyssen (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

Let F be a local field and G be GL2(F). Let V be the tensor product of three admissible, irreducible, infinite dimensional representations of G. The space L of trilinear, G-invariant forms on V has dimension 0 or 1. When it is 1, there is a non zero linear form in L, and one wants to find a test vector for this form, that is, a vector which is not in its kernel. Theoretically, there are many test vectors. The point is to get an explicit one. The first part of this paper is a survey about test vectors : how to get the dimension of L and which explicit test vectors are already known. The second part describes some applications to L-functions.

Domaines: Théorie des nombres [math.NT]

Louise Nyssen. Histoires de formes trilinéaires et de vecteurs test. Cohomologie l-adique et corps de nombres 10-14 d ecembre 2007, Apr 2007, CIRM, Marseille, France. pp.129-153. ⟨hal-00806005⟩