On the Holomorphy of Exterior-Square L-functions

Dustin Belt

On the Holomorphy of Exterior-Square L-functions

Number Theory 2012-06-08 v7

Authors: Dustin Belt

Abstract

In this paper, we show that the twisted partial exterior-square $L$ -function has a meromorphic continuation to the whole complex plane with only two possible simple poles at $s=1$ and $s=0$ . We do this by establishing the nonvanishing of the local zeta integrals defined by Jacquet and Shalika for any fixed $s_0$ . The even case is treated in detail. The odd case is treated briefly, in which case, the $L$ -function is shown to be entire.

Keywords

exterior-square L-function meromorphic continuation local zeta integral Jacquet-Shalika nonvanishing

Cite

@article{arxiv.1108.2200,
  title  = {On the Holomorphy of Exterior-Square L-functions},
  author = {Dustin Belt},
  journal= {arXiv preprint arXiv:1108.2200},
  year   = {2012}
}

Comments

Preprint of Doctoral Dissertation (Purdue University);v.6 due to a mistake that was found in the the previous version, the main result has been weakened a little, but still applies in most applications, 50 pages, 1 appendix

On the Holomorphy of Exterior-Square L-functions

Abstract

Keywords

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