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

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- by Chao-Ping Dong and Huajian Xue
- Represent. Theory
**21**(2017), 151-171 - DOI: https://doi.org/10.1090/ert/502
- Published electronically: August 21, 2017
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## Abstract:

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

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## Bibliographic Information

**Chao-Ping Dong**- Affiliation: Institute of Mathematics, Hunan University, Changsha 410082, People’s Republic of China
- MR Author ID: 850664
- Email: chaoping@hnu.edu.cn
**Huajian Xue**- Affiliation: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China
- Email: xuehuajian12@mails.ucas.ac.cn
- Received by editor(s): January 6, 2017
- Received by editor(s) in revised form: May 31, 2017
- Published electronically: August 21, 2017
- Additional Notes: The first author was supported by NSFC grant 11571097 and the China Scholarship Council.
- © Copyright 2017 American Mathematical Society
- Journal: Represent. Theory
**21**(2017), 151-171 - MSC (2010): Primary 22E47; Secondary 22E41
- DOI: https://doi.org/10.1090/ert/502
- MathSciNet review: 3687651