  We define the doubling zeta integral for smooth families of representations
of classical groups. Following this we prove a rationality result for these
zeta integrals and show that they satisfy a functional equation. Moreover, we
show that there exists an apropriate normalizing factor which allows us to
construct $\gamma$-factors for smooth families out of the functional equation.
We prove that under certain hypothesis, specializing this $\gamma$-factor at a
point of the family yields the $\gamma$-factor defined by Piateski-Shapiro and
Rallis.

Number Theory