The Whittaker period formula on metaplectic $\mathrm {SL}_2$
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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.References
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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
- MR Author ID: 964619
- Email: yannan.qiu@gmail.com
- Received by editor(s): January 27, 2017
- Received by editor(s) in revised form: April 6, 2017
- Published electronically: August 21, 2018
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 1083-1117
- MSC (2010): Primary 11F67, 11F70
- DOI: https://doi.org/10.1090/tran/7258
- MathSciNet review: 3885172