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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.06940 |
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| _version_ | 1866916402379620352 |
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| author | Xu, Peter |
| author_facet | Xu, Peter |
| contents | Using combinations of weight-1 and weight-2 of Kronecker-Eisenstein series to construct currents in the distributional de Rham complex of a squared elliptic curve, we find a simple explicit formula for the type II $(\text{GL}_2, \text{GL}_2)$ theta lift without smoothing, analogous to the classical formula of Siegel for periods of Eisenstein series. For $K$ a CM field, the same technique applies without change to obtain an analogous formula for the $(\text{GL}_2(K),K^\times)$ theta correspondence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06940 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Explicit formula for the $(\text{GL}_2, \text{GL}_2)$ theta lift via Bruhat decomposition Xu, Peter Number Theory Using combinations of weight-1 and weight-2 of Kronecker-Eisenstein series to construct currents in the distributional de Rham complex of a squared elliptic curve, we find a simple explicit formula for the type II $(\text{GL}_2, \text{GL}_2)$ theta lift without smoothing, analogous to the classical formula of Siegel for periods of Eisenstein series. For $K$ a CM field, the same technique applies without change to obtain an analogous formula for the $(\text{GL}_2(K),K^\times)$ theta correspondence. |
| title | Explicit formula for the $(\text{GL}_2, \text{GL}_2)$ theta lift via Bruhat decomposition |
| topic | Number Theory |
| url | https://arxiv.org/abs/2409.06940 |