On the Holomorphy of Exterior-Square L-functions

Details On the Holomorphy of Exterior-Square L-functions On the Holomorphy of Exterior-Square L-functions

2011-08-10

arxiv.org/abs/1108.2200v6

Mathematics

Number Theory

Preprint of Doctoral Dissertation (Purdue University);v.6 due to a mistake that was found in the the previous version, the mai

Scientific paper

In this paper we prove the holomorphy of the partial Exterior-Square $L$-function associated to an irreducible automorphic representation of $GL_r$. We use a result due to Jacquet (2010) that describes a certain class of a smooth vectors in the Whittaker model to establish the non-vanishing of the local zeta integrals defined by Jacquet and Shalika (1990). The even case is treated in detail, in which we establish the only possible poles of the $L$-function are at $s=0$ and $s=1$. The odd case is treated briefly, in which case, the $L$-function is shown to be entire.

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