Memoirs of the American Mathematical Society 1997; 218 pp; softcover Volume: 128 ISBN10: 0821805436 ISBN13: 9780821805435 List Price: US$57 Individual Members: US$34.20 Institutional Members: US$45.60 Order Code: MEMO/128/611
 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 (sphericalWhittaker case)
 Bibliography
