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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.
MSC (2010): Primary 33C10, 42B10
DOI: https://doi.org/10.1090/tran/7710
Published electronically: April 25, 2019
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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
Email: zhi.qi@zju.edu.cn

DOI: https://doi.org/10.1090/tran/7710
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