Geodesic
Poles of the Standard ${\mathcal{L}}$-function of $G_{2}$ and the Rallis–Schiffmann Lift
Canadian journal of mathematics, Tome 71 (2019) no. 5, pp. 1127-1161

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DOI

We characterize the cuspidal representations of $G_{2}$ whose standard ${\mathcal{L}}$-function admits a pole at $s=2$ as the image of the Rallis–Schiffmann lift for the commuting pair ($\widetilde{\text{SL}}_{2}$, $G_{2}$) in $\widetilde{\text{Sp}}_{14}$. The image consists of non-tempered representations. The main tool is the recent construction, by the second author, of a family of Rankin–Selberg integrals representing the standard ${\mathcal{L}}$-function.
DOI : 10.4153/CJM-2018-019-7
Mots-clés : automorphic representation, exceptional theta-lift, Siegel-Weil identity 
Gurevich, Nadya; Segal, Avner. Poles of the Standard ${\mathcal{L}}$-function of $G_{2}$ and the Rallis–Schiffmann Lift. Canadian journal of mathematics, Tome 71 (2019) no. 5, pp. 1127-1161. doi: 10.4153/CJM-2018-019-7
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     title = {Poles of the {Standard} ${\mathcal{L}}$-function of $G_{2}$ and the {Rallis{\textendash}Schiffmann} {Lift}},
     journal = {Canadian journal of mathematics},
     pages = {1127--1161},
     year = {2019},
     volume = {71},
     number = {5},
     doi = {10.4153/CJM-2018-019-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2018-019-7/}
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