L Functions for the Orthogonal Group (Memoirs of the American Mathematical Society)
Author： D. Ginzburg;I. Piatetski-Shapiro;S. Rallis
Publisher： American Mathematical Society
Publication year： 2013
E-ISBN: 9781470401962
P-ISBN(Paperback): 9780821805435
P-ISBN(Hardback): 9780821805435
Subject： O156.2 theory of algebraic numbers
Keyword： Algebra and Algebraic Geometry
Language： ENG
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L Functions for the Orthogonal Group (Memoirs of the American Mathematical Society)
Description
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.