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An exceptional Siegel–Weil formula and poles of the Spin L-function of
$\text{PGSp}_{6}$
- Part of
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- Journal:
- Compositio Mathematica / Volume 156 / Issue 6 / June 2020
- Published online by Cambridge University Press:
- 29 May 2020, pp. 1231-1261
- Print publication:
- June 2020
-
- Article
- Export citation
-
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 
$s=1$.
