A G_2-period of a Fourier coefficient of an Eisenstein series on E_6

Aaron Pollack Duke University Chen Wan Massachusetts Institute of Technology Michal Zydor University of Michigan

Number Theory Representation Theory mathscidoc:1908.24003

Israel Journal of Mathematics, to appear
We calculate a G_2-period of a Fourier coefficient of a cuspidal Eisenstein series on the split simply-connected group E_6, and relate this period to the Ginzburg-Rallis period of cusp forms on GL_6. This gives us a relation between the Ginzburg-Rallis period and the central value of the exterior cube L-function of GL_6.
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@inproceedings{aarona,
  title={A G_2-period of a Fourier coefficient of an Eisenstein series on E_6},
  author={Aaron Pollack, Chen Wan, and Michal Zydor},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190820235836158830428},
  booktitle={Israel Journal of Mathematics, to appear},
}
Aaron Pollack, Chen Wan, and Michal Zydor. A G_2-period of a Fourier coefficient of an Eisenstein series on E_6. In Israel Journal of Mathematics, to appear. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190820235836158830428.
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