The Gross--Kohnen--Zagier theorem via $p$-adic uniformization
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917624307253248 |
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| author | Beneish, Lea Darmon, Henri Gehrmann, Lennart Roset, Martí |
| author_facet | Beneish, Lea Darmon, Henri Gehrmann, Lennart Roset, Martí |
| contents | This article gives a new proof of the Gross--Kohnen--Zagier theorem for Shimura curves which exploits the $p$-adic uniformization of Cerednik--Drinfeld. The explicit description of CM points via this uniformization leads to an expression relating the Gross--Kohnen--Zagier generating series to the ordinary projection of the first derivative, with respect to a weight variable, of a $p$-adic family of positive definite ternary theta series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18688 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Gross--Kohnen--Zagier theorem via $p$-adic uniformization Beneish, Lea Darmon, Henri Gehrmann, Lennart Roset, Martí Number Theory This article gives a new proof of the Gross--Kohnen--Zagier theorem for Shimura curves which exploits the $p$-adic uniformization of Cerednik--Drinfeld. The explicit description of CM points via this uniformization leads to an expression relating the Gross--Kohnen--Zagier generating series to the ordinary projection of the first derivative, with respect to a weight variable, of a $p$-adic family of positive definite ternary theta series. |
| title | The Gross--Kohnen--Zagier theorem via $p$-adic uniformization |
| topic | Number Theory |
| url | https://arxiv.org/abs/2403.18688 |