On the Fourier Transform of Bessel Functions over Complex Numbers---II: the General Case
Classical Analysis and ODEs
2018-08-21 v3
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.
Keywords
Cite
@article{arxiv.1607.01098,
title = {On the Fourier Transform of Bessel Functions over Complex Numbers---II: the General Case},
author = {Zhi Qi},
journal= {arXiv preprint arXiv:1607.01098},
year = {2018}
}
Comments
25 pages, to appear in Trans. Amer. Math. Soc