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

Published 12 Apr 2019 in math.NT and math.RT | (1904.06000v1)

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 $PGSp_6$ 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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Authors (2)

  1. Wee Teck Gan 
  2. Gordan Savin 

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