Electronic ISBN:  9781470401962 
Product Code:  MEMO/128/611.E 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $36.00 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 128; 1997; 218 ppMSC: Primary 11;
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.
ReadershipGraduate students and research mathematicians interested in number theory.

Table of Contents

Chapters

0. Introduction

1. Basic data

2. Support ideals

3. Certain Jacquet functors

4. Global theory

5. Support ideals (II)

6. Calculation of local factors

7. Determination of $\gamma $factors (spherical case)

8. Determination of $\gamma $factors (sphericalWhittaker case)


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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.

Chapters

0. Introduction

1. Basic data

2. Support ideals

3. Certain Jacquet functors

4. Global theory

5. Support ideals (II)

6. Calculation of local factors

7. Determination of $\gamma $factors (spherical case)

8. Determination of $\gamma $factors (sphericalWhittaker case)