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Title: An exceptional Siegel–Weil formula and poles of the Spin L-function of
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 $s=1$ .  more » « less
Award ID(s):
1901745
PAR ID:
10232628
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Compositio Mathematica
Volume:
156
Issue:
6
ISSN:
0010-437X
Page Range / eLocation ID:
1231 to 1261
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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