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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
L Functions for the Orthogonal Group
eBook ISBN:  978-1-4704-0196-2
Product Code:  MEMO/128/611.E
List Price: $60.00
MAA Member Price: $54.00
AMS Member Price: $36.00
L Functions for the Orthogonal Group
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$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
eBook 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.

    Readership

    Graduate 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 (spherical-Whittaker case)
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    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.

Readership

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 publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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