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$$L$$ Functions for the Orthogonal Group
D. Ginzburg and I. Piatetski-Shapiro, Yale University, New Haven, CT, and S. Rallis, Columbus, OH
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Memoirs of the American Mathematical Society
1997; 218 pp; softcover
Volume: 128
ISBN-10: 0-8218-0543-6
ISBN-13: 978-0-8218-0543-5
List Price: US$60 Individual Members: US$36
Institutional Members: US\$48
Order Code: MEMO/128/611

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.

Graduate students and research mathematicians interested in number theory.

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