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


Authors: Chao-Ping Dong and Huajian Xue
Journal: Represent. Theory 21 (2017), 151-171
MSC (2010): Primary 22E47; Secondary 22E41
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.


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Additional Information

Chao-Ping Dong
Affiliation: Institute of Mathematics, Hunan University, Changsha 410082, People’s Republic of China
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

DOI: https://doi.org/10.1090/ert/502
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.
Article copyright: © Copyright 2017 American Mathematical Society

American Mathematical Society