On the Fourier transform of regularized Bessel functions on complex numbers and Beyond Endoscopy over number fields
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arXiv
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866915961418809344 |
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| author | Qi, Zhi |
| author_facet | Qi, Zhi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1810_11984 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On the Fourier transform of regularized Bessel functions on complex numbers and Beyond Endoscopy over number fields Qi, Zhi Number Theory Classical Analysis and ODEs 33C10, 42B10, 33C05 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. |
| title | On the Fourier transform of regularized Bessel functions on complex numbers and Beyond Endoscopy over number fields |
| topic | Number Theory Classical Analysis and ODEs 33C10, 42B10, 33C05 |
| url | https://arxiv.org/abs/1810.11984 |