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An exceptional Siegel–Weil formula and poles of the Spin L-function of $\text{PGSp}_{6}$
Published online by Cambridge University Press: 29 May 2020
Abstract
We show a Siegel–Weil formula in the setting of exceptional theta correspondence. Using this, together with a new Rankin–Selberg integral for the Spin L-function of $\text{PGSp}_{6}$ discovered by Pollack, we prove that a cuspidal representation of $\text{PGSp}_{6}$ is a (weak) functorial lift from the exceptional group $G_{2}$ if its (partial) Spin L-function has a pole at $s=1$.
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