Poles of the Standard L-function of G₂ and the Rallis-Schiffmann Lift

2016/06/29 by Gurevich, Nadya, Segal, Avner
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1606.09069

Abstract

We characterize the cuspidal representations of G₂ whose standard L-function admits a pole at s=2 as the image of Rallis-Schiffmann lift for the commuting pair (\widetildeSL₂, G₂) in \widetildeSp₁₄. 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.

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