English

On the nonvanishing hypothesis for Rankin-Selberg convolutions for $\mathrm{GL}_n(\mathbb C)\times \mathrm{GL}_n(\mathbb C)$

Representation Theory 2016-12-30 v1

Abstract

Inspired by Sun's breakthrough in establishing the nonvanishing hypothesis for Rankin-Selberg convolutions for the groups GLn(R)×GLn1(R)\mathrm{GL}_n (\mathbb R)\times \mathrm{GL}_{n-1} (\mathbb R) and GLn(C)×GLn1(C)\mathrm{GL}_n (\mathbb C)\times \mathrm{GL}_{n-1} (\mathbb C), we confirm it for GLn(C)×GLn(C)\mathrm{GL}_{n} (\mathbb C)\times \mathrm{GL}_n (\mathbb C) at the central critical point.

Keywords

Cite

@article{arxiv.1612.09107,
  title  = {On the nonvanishing hypothesis for Rankin-Selberg convolutions for $\mathrm{GL}_n(\mathbb C)\times \mathrm{GL}_n(\mathbb C)$},
  author = {Chao-Ping Dong and Huajian Xue},
  journal= {arXiv preprint arXiv:1612.09107},
  year   = {2016}
}

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21 pages