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The Spin L-function on GSp6 Via a non-unique model
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Journal Article
The Spin L-function on GSp6 Via a non-unique model
2018
Overview
We give two global integrals that unfold to a non-unique model and represent the partial Spin $L$-function on ${\\rm PGSp}_6$. We deduce that for a wide class of cuspidal automorphic representations $\\pi$, the partial Spin $L$-function is holomorphic except for a possible simple pole at $s=1$, and that the presence of such a pole indicates that $\\pi$ is an exceptional theta lift from ${\\rm G}_2$. These results utilize and extend previous work of Gan and Gurevich, who introduced one of the global integrals and proved these facts for a special subclass of these $\\pi$ upon which the aforementioned model becomes unique. The other integral can be regarded as a higher rank analogue of the integral of Kohnen-Skoruppa on ${\\rm GSp}_4$.
Publisher
Johns Hopkins University Press
Subject
