A generalized Rubin formula for Hecke characters
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912179224051712 |
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| author | Longo, Matteo Vigni, Stefano Wang, Shilun |
| author_facet | Longo, Matteo Vigni, Stefano Wang, Shilun |
| contents | The goal of this paper is to generalize Rubin's theorem on values of Katz's $p$-adic $L$-function outside the range of interpolation from the case of Hecke characters of CM elliptic curves to more general self-dual algebraic Hecke characters. We follow the approach by Bertolini-Darmon-Prasanna, based on generalized Heegner cycles, which we extend from characters of imaginary quadratic fields of infinity type $(1,0)$ to characters of infinity type $(1+\ell,-\ell)$ for an integer $\ell\geq0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03673 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A generalized Rubin formula for Hecke characters Longo, Matteo Vigni, Stefano Wang, Shilun Number Theory Algebraic Geometry 11G40, 14C15 The goal of this paper is to generalize Rubin's theorem on values of Katz's $p$-adic $L$-function outside the range of interpolation from the case of Hecke characters of CM elliptic curves to more general self-dual algebraic Hecke characters. We follow the approach by Bertolini-Darmon-Prasanna, based on generalized Heegner cycles, which we extend from characters of imaginary quadratic fields of infinity type $(1,0)$ to characters of infinity type $(1+\ell,-\ell)$ for an integer $\ell\geq0$. |
| title | A generalized Rubin formula for Hecke characters |
| topic | Number Theory Algebraic Geometry 11G40, 14C15 |
| url | https://arxiv.org/abs/2501.03673 |