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