Hilbert Poincaré series and kernels for products of $L$-functions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913183218794496 |
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| author | Zhang, Mingkuan Zhang, Yichao |
| author_facet | Zhang, Mingkuan Zhang, Yichao |
| contents | We study Hilbert Poincaré series associated to general seed functions and construct Cohen's kernels and double Eisenstein series as series of Hilbert Poincaré series. Then we calculate the Rankin-Cohen brackets of Hilbert Poincaré series and Hilbert modular forms and extend Zagier's kernel formula to totally real number fields. Finally, we show that the Rankin-Cohen brackets of two different types of Eisenstein series are special values of double Eisenstein series up to a constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01282 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hilbert Poincaré series and kernels for products of $L$-functions Zhang, Mingkuan Zhang, Yichao Number Theory We study Hilbert Poincaré series associated to general seed functions and construct Cohen's kernels and double Eisenstein series as series of Hilbert Poincaré series. Then we calculate the Rankin-Cohen brackets of Hilbert Poincaré series and Hilbert modular forms and extend Zagier's kernel formula to totally real number fields. Finally, we show that the Rankin-Cohen brackets of two different types of Eisenstein series are special values of double Eisenstein series up to a constant. |
| title | Hilbert Poincaré series and kernels for products of $L$-functions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2401.01282 |