An exceptional Siegel-Weil formula and poles of the Spin L-function of $PGS{p}_6$

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 $PGS{p}_6$ discovered by A. Pollack, we prove that a cuspidal representation of $PGS{p}_6$ is a (weak) functorial lift from the exceptional group $G_2$ if its (partial) Spin L-function has a pole at $s=1$.

References in corpus (1)

• Eisenstein series arising from Jordan algebras

Cited by in corpus (2)

• Algebraic cycles and functorial lifts from $G_2$ to ${\mathrm{PGSp}}_6$
• Generalised Whittaker models as instances of relative Langlands duality