On the Fourier transform of regularized Bessel functions on complex numbers and Beyond Endoscopy over number fields
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2018
- DOI:
- 10.48550/arXiv.1810.11984
- arXiv:
- arXiv:1810.11984
- Bibcode:
- 2018arXiv181011984Q
- Keywords:
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- Mathematics - Number Theory;
- Mathematics - Classical Analysis and ODEs;
- 33C10;
- 42B10;
- 33C05
- E-Print:
- 26 pages. An appendix added. Small errors corrected. To appear in IMRN