An exceptional Siegel-Weil formula and poles of the Spin L-function of $PGSp_6$

12 Apr 2019  ·  Gan Wee Teck, Savin Gordan ·

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 $PGSp_6$ discovered by A. Pollack, we prove that a cuspidal representation of $PGSp_6$ 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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Number Theory Representation Theory