Langlands-Shahidi Method and Poles of Automorphic L-Functions: Application to Exterior Square L-Functions

Kim, Henry H.

Canadian journal of mathematics, Tome 51 (1999) no. 4, pp. 835-849

Résumé

In this paper we use Langlands-Shahidi method and the result of Langlands which says that non self-conjugate maximal parabolic subgroups do not contribute to the residual spectrum, to prove the holomorphy of several completed automorphic $L$ -functions on the whole complex plane which appear in constant terms of the Eisenstein series. They include the exterior square $L$ -functions of $\text{G}{{\text{L}}_{\text{n}}},\,n$ odd, the Rankin-Selberg $L$ -functions of $\text{G}{{\text{L}}_{n}}\times \,\text{G}{{\text{L}}_{m}},\,n\,\ne \,m$ , and $L$ -functions $L\left( s,\,\sigma ,\,r \right)$ , where $\sigma $ is a generic cuspidal representation of $\text{S}{{\text{O}}_{10}}$ and $r$ is the half-spin representation of GSpin $\left( 10,\,\mathbb{C} \right)$ . The main part is proving the holomorphy and non-vanishing of the local normalized intertwining operators by reducing them to natural conjectures in harmonic analysis, such as standard module conjecture.

Détail

DOI : 10.4153/CJM-1999-036-0

Mots-clés : 11F, 22E

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