On the adjoint L-function of the p-adic GSp(4)

Details On the adjoint L-function of the p-adic GSp(4) On the adjoint L-function of the p-adic GSp(4)

2007-03-07

arxiv.org/abs/math/0703181v2

Mathematics

Number Theory

small corrections and improvements; to appear in J. Number Theory

Scientific paper

We explicitly compute the adjoint L-function of those L-packets of representations of the group GSp(4) over a p-adic field of characteristic zero that contain non-supercuspidal representations. As an application we verify a conjecture of Gross-Prasad and Rallis in this case. The conjecture states that the adjoint L-function has a pole at s=1 if and only if the L-packet contains a generic representation.

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