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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The Whittaker period formula on metaplectic $ \mathrm{SL}_2$


Author: Yannan Qiu
Journal: Trans. Amer. Math. Soc. 371 (2019), 1083-1117
MSC (2010): Primary 11F67, 11F70
DOI: https://doi.org/10.1090/tran/7258
Published electronically: August 21, 2018
MathSciNet review: 3885172
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Abstract: The Whittaker period formula on $ \widetilde {\mathrm {SL}}_2(\mathbb{A}_F)$ was previously established only when the base field $ F$ is totally real. We present a new simple proof that works for all base number fields. Our local argument is uniform at every local place of $ F$, based on the isometry property of quadratic Fourier transform and the estimates of matrix coefficients and Whittaker functions imposed by the unitarity of the local representations.


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Additional Information

Yannan Qiu
Affiliation: Department of Mathematics and Statistics, Neville Hall, University of Maine, Orono, Maine 04469
Address at time of publication: Department of Mathematics, Southern University of Science and Technology, 1088 Xueyuan Road, Nanshan District, Shenzhen, Guangdong 518055, China
Email: yannan.qiu@gmail.com

DOI: https://doi.org/10.1090/tran/7258
Received by editor(s): January 27, 2017
Received by editor(s) in revised form: April 6, 2017
Published electronically: August 21, 2018
Article copyright: © Copyright 2018 American Mathematical Society