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Representation Theory

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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.
Published electronically: August 21, 2017
MathSciNet review: 3687651
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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
MR Author ID: 850664

Huajian Xue
Affiliation: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

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