**Memoirs of the American Mathematical Society**

1997;
218 pp;
Softcover

MSC: Primary 11;

Print ISBN: 978-0-8218-0543-5

Product Code: MEMO/128/611

List Price: $60.00

AMS Member Price: $36.00

MAA member Price: $54.00

**Electronic ISBN: 978-1-4704-0196-2
Product Code: MEMO/128/611.E**

List Price: $60.00

AMS Member Price: $36.00

MAA member Price: $54.00

# \(L\) Functions for the Orthogonal Group

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*D. Ginzburg; I. Piatetski-Shapiro; S. Rallis*

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.

#### Readership

Graduate students and research mathematicians interested in number theory.

#### Table of Contents

# Table of Contents

## $L$ Functions for the Orthogonal Group

- Table of Contents vii8 free
- §0. Introduction 110 free
- §1. Basic Data 1423 free
- §2. Support Ideals 2534
- §3. Certain Jacquet Functors 3140
- §4. Global Theory 5564
- §4.1 Global Theory 5564
- §4.2 Spherical-Whittaker Case (I) 6574
- §4.3 Spherical-Whittaker Models (II) 6776
- §5. Support Ideals (II) 91100
- §6. Calculation of local factors 154163
- §7. Determination of γ-factors (Spherical Case) 170179
- §8. Determination of γ-factors (Spherical-Whittaker Case) 197206
- §9 Bibliography 218227