On the Fourier Transform of Bessel Functions over Complex Numbers---II: the General Case

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.

25 pages, to appear in Trans. Amer. Math. Soc