On periods of Elliptic curves
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911741700472832 |
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| author | Salaza, Daniel Barrera Llerena-Córdova, Juan-Pablo |
| author_facet | Salaza, Daniel Barrera Llerena-Córdova, Juan-Pablo |
| contents | Let $E$ be an elliptic curve over $\mathbb{Q}$ having split multiplicative reduction at a prime number $p$. We describe the tame part of the $\mathcal{L}$-invariant of $E$ at $p$ in terms of automorphic $p$-adic periods introduced in the work of Darmon. More precisely, we prove an equality of refined $\mathcal{L}$-invariants using twisted versions of refined exceptional zero conjectures. When the conductor of the elliptic curve is exactly $p$ and the automorphic period is attached to an optimal embedding of conductor $1$ then we prove this equality unconditionally by using the work of de-Shalit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_02254 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On periods of Elliptic curves Salaza, Daniel Barrera Llerena-Córdova, Juan-Pablo Number Theory 11G05, 14H52, 11G18 Let $E$ be an elliptic curve over $\mathbb{Q}$ having split multiplicative reduction at a prime number $p$. We describe the tame part of the $\mathcal{L}$-invariant of $E$ at $p$ in terms of automorphic $p$-adic periods introduced in the work of Darmon. More precisely, we prove an equality of refined $\mathcal{L}$-invariants using twisted versions of refined exceptional zero conjectures. When the conductor of the elliptic curve is exactly $p$ and the automorphic period is attached to an optimal embedding of conductor $1$ then we prove this equality unconditionally by using the work of de-Shalit. |
| title | On periods of Elliptic curves |
| topic | Number Theory 11G05, 14H52, 11G18 |
| url | https://arxiv.org/abs/2606.02254 |