Isotypic decomposition of the cohomology and factorization of the zeta functions of Dwork hypersurfaces

The aim of this article is to illustrate, on the Dwork hypersurfaces xn1+· · ·+x n n−nψx1 . . . xn = 0 (with n an integer ≥ 3 and ψ ∈ F∗ q a parameter satisfying ψ n 6= 1), how the study of the representation of a finite group of automorphisms of a hypersurface in its etale cohomology allows to factor its zeta function.