Poles of the Standard -function of and the Rallis–Schiffmann Lift

We characterize the cuspidal representations of G₂ whose standard L -function admits a pole at $s=2$ as the image of the Rallis–Schiffmann lift for the commuting pair ( SL₂ , G₂ ) in Sp₁₄ . 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 L -function.