An exceptional Siegel–Weil formula and poles of the Spin L-function of
| Autor: | Gordan Savin, Wee Teck Gan |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Compositio Mathematica. 156:1231-1261 |
| ISSN: | 1570-5846 0010-437X |
| DOI: | 10.1112/s0010437x20007186 |
| Popis: | 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 $s=1$. |
| Databáze: | OpenAIRE |
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