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$L$ Functions for the Orthogonal Group

D. Ginzburg Yale University, New Haven, CT
I. Piatetski-Shapiro Yale University, New Haven, CT
S. Rallis Columbus, OH
Available Formats:
Electronic ISBN: 978-1-4704-0196-2
Product Code: MEMO/128/611.E
List Price: $60.00 MAA Member Price:$54.00
AMS Member Price: $36.00 Click above image for expanded view$L$Functions for the Orthogonal Group D. Ginzburg Yale University, New Haven, CT I. Piatetski-Shapiro Yale University, New Haven, CT S. Rallis Columbus, OH Available Formats:  Electronic ISBN: 978-1-4704-0196-2 Product Code: MEMO/128/611.E  List Price:$60.00 MAA Member Price: $54.00 AMS Member Price:$36.00
• Book Details

Memoirs of the American Mathematical Society
Volume: 1281997; 218 pp
MSC: 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.

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 (spherical-Whittaker case)
• Requests

Review Copy – for reviewers who would like to review an AMS book
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Accessibility – to request an alternate format of an AMS title
Volume: 1281997; 218 pp
MSC: 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.

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 (spherical-Whittaker case)
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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