On the tempered L-function conjecture

Details On the tempered L-function conjecture On the tempered L-function conjecture

2009-08-05

arxiv.org/abs/0908.0699v4

Mathematics

Number Theory

19 pages, 13 figures, minor misleading misprints corrected and an address updated

Scientific paper

We give a general proof of Shahidi's tempered L-function conjecture, which has previously been known in all but one case. One of the consequences is the standard modules conjecture for p-adic groups, which means that the Langlands quotient of a standard module is generic if and only if the standard module is irreducible and the inducing data generic. We have also included the result that every generic tempered representation of a p-adic group is a sub-representation of a representation parabolically induced from a generic supercuspidal representation with a non-negative real central character.

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