  We consider the one-parameter family of hypersurfaces in $\Pj^5$ with
projective equation (X_1^5+X_2^5+X_3^5+X_4^5+X_5^5) = 5\lambda X_1 X_2... X_5,
(writing $\lambda$ for the parameter), proving that the Galois representations
attached to their cohomologies are potentially automorphic, and hence that the
zeta function of the family has meromorphic continuation throughout the complex
plane.
