Introduction and preliminaries The integrals to be studied Estimates for Whittaker functions on $G_\ell$ (nonarchimedean case) Estimates for Whittaker functions on $G_\ell$ (archimedean case) Convergence of the integrals (nonarchimedean case) Convergence of the integrals (archimedean case) $A(W,\xi_{\tau,s})$ can be made constant (nonarchimedean case) An analog in the archimedean case Uniqueness theorems Application of the intertwining operator Definition of local factors Multiplicativity of the $\gamma$-factor (case $\ell < n$, first variable) The unramified computation.
