Triple product $p$-adic $L$-functions for finite slope families and a $p$-adic Gross-Zagier formula
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929292044140544 |
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| author | Huang, Ting-Han |
| author_facet | Huang, Ting-Han |
| contents | In this paper, we generalize two results of H. Darmon and V. Rotger on triple product $p$-adic $L$-functions associated with Hida families to finite slope families. We first prove a $p$-adic Gross-Zagier formula, then demonstrate an application to a special case of the equivariant Birch and Swinnerton-Dyer conjecture for supersingular elliptic curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18620 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Triple product $p$-adic $L$-functions for finite slope families and a $p$-adic Gross-Zagier formula Huang, Ting-Han Number Theory 11F12, 11G05, 11G35, 11G40 In this paper, we generalize two results of H. Darmon and V. Rotger on triple product $p$-adic $L$-functions associated with Hida families to finite slope families. We first prove a $p$-adic Gross-Zagier formula, then demonstrate an application to a special case of the equivariant Birch and Swinnerton-Dyer conjecture for supersingular elliptic curves. |
| title | Triple product $p$-adic $L$-functions for finite slope families and a $p$-adic Gross-Zagier formula |
| topic | Number Theory 11F12, 11G05, 11G35, 11G40 |
| url | https://arxiv.org/abs/2403.18620 |