Entireness ofL-Functions ofphi-Sheaves on Affine Complete Intersections Original Research Article

In a previous article, the authors showed that theL-function attached to aπ-adicphi-sheaf is meromorphic in a certain disk depending on the convergence condition of thephi-sheaf. That disk is in general best possible. The purpose of the present article is to show that for an affine complete intersection, either theL-function or its reciprocal is actually analytic (i.e., without poles) in the same disk.