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arXiv · 1810.11984

On the Fourier transform of regularized Bessel functions on complex numbers and Beyond Endoscopy over number fields

Zhi Qi
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Abstract

In this article, we prove certain Weber-Schafheitlin type integral formulae for Bessel functions over complex numbers. A special case is a formula for the Fourier transform of regularized Bessel functions on complex numbers. This is applied to extend the work of A. Venkatesh on Beyond Endoscopy for $\mathrm{Sym}^2$ on $\mathrm{GL}_2$ from totally real to arbitrary number fields.

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Zhi Qi. 2026-04-27. On the Fourier transform of regularized Bessel functions on complex numbers and Beyond Endoscopy over number fields. https://doi.org/10.1093/imrn%2Frnz205

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