On twisted Koecher-Maass series and its integral Kernel
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910731137449984 |
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| author | Herrera, Fernando |
| author_facet | Herrera, Fernando |
| contents | We establish the integral kernel associated with the Koecher-Maass series of degree three twisted by an Eisenstein series. We prove that such a kernel admits an analytic continuation and determine its functional equations. We find a second representation of this kernel using Poincaré series. As an application, we give another proof of the analytic properties for the twisted Koecher-Maass series. Furthermore, we generalize a result due to Siegel related to the Lipschitz summation formula on the Siegel space of degree three. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05129 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On twisted Koecher-Maass series and its integral Kernel Herrera, Fernando Number Theory 11F68, 11F46, 11M32 We establish the integral kernel associated with the Koecher-Maass series of degree three twisted by an Eisenstein series. We prove that such a kernel admits an analytic continuation and determine its functional equations. We find a second representation of this kernel using Poincaré series. As an application, we give another proof of the analytic properties for the twisted Koecher-Maass series. Furthermore, we generalize a result due to Siegel related to the Lipschitz summation formula on the Siegel space of degree three. |
| title | On twisted Koecher-Maass series and its integral Kernel |
| topic | Number Theory 11F68, 11F46, 11M32 |
| url | https://arxiv.org/abs/2412.05129 |