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Transactions of the American Mathematical Society

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On the Fourier transform of Bessel functions over complex numbers—II: The general case


Author: Zhi Qi
Journal: Trans. Amer. Math. Soc. 372 (2019), 2829-2854
MSC (2010): Primary 33C10, 42B10
DOI: https://doi.org/10.1090/tran/7710
Published electronically: April 25, 2019
MathSciNet review: 3988595
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Abstract: In this paper, we prove an exponential integral formula for the Fourier transform of Bessel functions over complex numbers, along with a radial exponential integral formula. The former will enable us to develop the complex spectral theory of the relative trace formula for the Shimura–Waldspurger correspondence and extend the Waldspurger formula from totally real fields to arbitrary number fields.


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Additional Information

Zhi Qi
Affiliation: School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, People’s Republic of China
MR Author ID: 963773
ORCID: 0000-0002-2454-3291
Email: zhi.qi@zju.edu.cn

Keywords: Bessel functions, exponential integral formulae
Received by editor(s): November 9, 2017
Received by editor(s) in revised form: August 16, 2018
Published electronically: April 25, 2019
Article copyright: © Copyright 2019 American Mathematical Society