# L Functions for the Orthogonal Group (Memoirs of the American Mathematical Society No. 611)

By: D. Ginzburg (author), etc. (author), I. Piatetski-Shapiro (author), s. Rallis (author)Paperback

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### Description

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.

### Contents

Introduction Basic data Support ideals Certain Jacquet functors Global theory Support ideals (II) Calculation of local factors Determination of $\gamma$-factors (spherical case) Determination of $\gamma$-factors (spherical-Whittaker case) Bibliography.

### Product Details

• publication date: 15/08/1997
• ISBN13: 9780821805435
• Format: Paperback
• Number Of Pages: 218
• ID: 9780821805435
• weight: 397
• ISBN10: 0821805436

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