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\(L\) Functions for the Orthogonal Group
D. Ginzburg and I. Piatetski-Shapiro, Yale University, New Haven, CT, and S. Rallis, Columbus, OH
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Memoirs of the American Mathematical Society
1997; 218 pp; softcover
Volume: 128
ISBN-10: 0-8218-0543-6
ISBN-13: 978-0-8218-0543-5
List Price: US$57
Individual Members: US$34.20
Institutional Members: US$45.60
Order Code: MEMO/128/611
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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.

Readership

Graduate students and research mathematicians interested in number theory.

Table of 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
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