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International Mathematics Research Papers (2006) Vol. 2006 : article ID 68213, 74 pages, doi:10.1155/IMRP/2006/68213
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Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.

The spin L-function of quasi-split D4

Wee Teck Gan and Joseph Hundley

Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA E-mail address: wgan{at}math.ucsd.edu
Department of Mathematics, Penn State University University Park, State College, PA 16802, USA E-mail address: hundley{at}math.psu.edu

We construct a multivariable Rankin-Selberg integral for the Spin L-function of a globally generic cuspidal representation of an arbitrary quasi-split group of type D4. This proves the meromorphic continuation of this L-function. When the quasi-split group of type D4 is associated to a cubic field extention, this L-function cannot be analyzed by the Langlands-Shahidi method.


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