Poles of the Standard $\mathcal{L}$-function of $G_2$ and the   Rallis-Schiffmann Lift
  We characterize the cuspidal representations of $G_2$ whose standard $\mathcal{L}$-function admits a pole at $s=2$ as the image of Rallis-Schiffmann lift for the commuting pair $\left(\widetilde{SL_2}, G_2\right)$ in $\widetilde{Sp_{14}}$. 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. 
Nadya Gurevich and Avner Segal
math.RT math.NT