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Canad. J. Math. Vol. 54 (4), 2002 pp. 673693 Local L-Functions for Split Spinor Groups

Summary: Canad. J. Math. Vol. 54 (4), 2002 pp. 673693
Local L-Functions for Split Spinor Groups
Mahdi Asgari
Abstract. We study the local L-functions for Levi subgroups in split spinor groups defined via the
Langlands-Shahidi method and prove a conjecture on their holomorphy in a half plane. These results
have been used in the work of Kim and Shahidi on the functorial product for GL2 GL3.
1 Introduction
The purpose of this work is to prove a conjecture on the holomorphy of local Lang-
lands L-functions defined via the Langlands-Shahidi method in split spinor groups.
These local factors appear in the Euler products of global automorphic L-functions
and information about their holomorphy is frequently exploited in order to prove
results about the analytic properties of global objects. In particular, in a recent im-
portant work, H. Kim and F. Shahidi have used some cases of our result here in order
to handle some local problems in their long-awaited result on the existence of sym-
metric cube cusp forms on GL2 (cf. [11], [12]).
Apart from trace formula methods, two methods have been suggested to study
these factors: the Rankin-Selberg method which uses "zeta integrals" and the
Langlands-Shahidi method which uses "Eisenstein series". Our focus in this work
is on the latter [13], [16], [18], [20].
Let M be a (quasi) split connected reductive linear algebraic group defined over


Source: Asgari, Mahdi - Department of Mathematics, Oklahoma State University


Collections: Mathematics