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International Mathematics Research Notices (2006) Vol. 2006 : article ID 64069, 26 pages, doi:10.1155/IMRN/2006/64069
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Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.

On the fundamental automorphic L-functions of SO(2n + 1)

Dihua Jiang

School of Mathematics, University of Minnesota Minneapolis, MN 55455, USA E-mail address: dhjiang{at}math.umn.edu

We prove that the second fundamental L-functions attached to irreducible generic unitary cuspidal automorphic representations of SO2n+1 have meromorphic continuation to the whole complex plane and satisfy the functional equation as expected by the Langlands conjecture, using the recent progress in the Langlands functorial transfer for classical groups. Then we study the relation between the order of the pole at s = 1 of the fundamental L-functions and the endoscopy structures of the irreducible generic unitary cuspidal automorphic representations of SO2n+1, under the assumption of the Langlands conjecture for higher fundamental L-functions.


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