David Ginzburg 
$L$ Functions for the Orthogonal Group [PDF ebook] 

In this book, the authors establish global Rankin Selberg integrals which determine the standard $L$ function for the group $GL_r/times G’$, where $G’$ is an isometry group of a nondegenerate symmetric form. The class of automorphic representations considered here is for any pair $/prod_1/otimes/prod_2$ where $/prod_1$ is generic cuspidal for $GL_r(A)$ and $/prod_2$ is cuspidal for $G'(A)$. The construction of these $L$ functions involves the use of certain new "models" of local representations; these models generalize the usual generic models. The authors also compute local unramified factors in a new way using geometric ideas.