  We extend the theory of local constants to l-adic families of representations
of GL_n(F) where F is a p-adic field with l not equal to p. We construct zeta
integrals and gamma factors for representations coming from the conjectural
"local Langlands correspondence in families" of Emerton-Helm, proving a
rationality result and functional equation. We also construct a universal gamma
factor with coefficients in the integral Bernstein center.
