On a Rankin-Selberg integral of the L-function for $\widetilde{SL}_2\times GL_2$

Qing Zhang

On a Rankin-Selberg integral of the L-function for $\widetilde{SL}_2\times GL_2$

Number Theory 2023-02-14 v1

Authors: Qing Zhang

Abstract

We present a Rankin-Selberg integral on the exceptional group $G_2$ which represents the L-function for generic cuspidal representations of $\widetilde{SL}_2\times GL_2$ . As an application, we show that certain Fourier-Jacobi type periods on $G_2$ are non-vanishing.

Keywords

rankin-selberg integral l-function g_2 tilde{sl}_2 times gl_2 cuspidal representations fourier-jacobi periods

Cite

@article{arxiv.2009.05980,
  title  = {On a Rankin-Selberg integral of the L-function for $\widetilde{SL}_2\times GL_2$},
  author = {Qing Zhang},
  journal= {arXiv preprint arXiv:2009.05980},
  year   = {2023}
}

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