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DC Field | Value | Language |
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dc.contributor.author | Gatti, Francesca | - |
dc.contributor.author | Guitart Morales, Xavier | - |
dc.contributor.author | Masdeu Sabaté, Marc | - |
dc.contributor.author | Rotger, Víctor | - |
dc.date.accessioned | 2023-09-21T07:52:50Z | - |
dc.date.available | 2023-09-21T07:52:50Z | - |
dc.date.issued | 2021 | - |
dc.identifier.issn | 1246-7405 | - |
dc.identifier.uri | http://hdl.handle.net/2445/202122 | - |
dc.description.abstract | The main purpose of this note is to understand the arithmetic encoded in the special value of the $p$-adic $L$-function $E_p^g$ (f, $\left.\mathbf{g}, \mathbf{h}\right)$ associated to a triple of modular forms $(f, g, h)$ of weights $(2,1,1)$, in the case where the classical $L$-function $L(f \otimes g \otimes h, s)$ (which typically has sign +1$)$ does not vanish at its central critical point $s=1$. When $f$ corresponds to an elliptic curve $E / \mathbb{Q}$ and the classical $L$-function vanishes, the Elliptic Stark Conjecture of Darmon-Lauder-Rotger predicts that $E_p^g$ (f, $\left.\mathbf{g}, \mathbf{h}\right)(2,1,1)$ is either 0 (when the order of vanishing of the complex $L$-function is $>2$ ) or related to logarithms of global points on $E$ and a certain Gross-Stark unit associated to $g$ (when the order of vanishing is exactly 2). We complete the picture proposed by the Elliptic Stark Conjecture by providing a formula for the value $E_p^g(\mathbf{f}, \mathbf{g}, \mathbf{h})(2,1,1)$ in the case where $L(f \otimes g \otimes h, 1) \neq 0$. | - |
dc.format.extent | 26 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Société Arithmétique de Bordeaux and Centre Mersenne | - |
dc.relation.isformatof | Reproducció del document publicat a: https://doi.org/10.5802/jtnb.1179 | - |
dc.relation.ispartof | Journal de Théorie des Nombres de Bordeaux, 2021, vol. 33, p. 809-834 | - |
dc.relation.uri | https://doi.org/10.5802/jtnb.1179 | - |
dc.rights | cc-by-nd (c) Gatti, Francesca et al., 2021 | - |
dc.rights.uri | https://creativecommons.org/licenses/by-nd/4.0/ | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Funcions L | - |
dc.subject.classification | Anàlisi p-àdica | - |
dc.subject.other | L-functions | - |
dc.subject.other | p-adic analysis | - |
dc.title | Special values of triple-product -adic L-functions and non-crystalline diagonal classes | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/publishedVersion | - |
dc.identifier.idgrec | 720804 | - |
dc.date.updated | 2023-09-21T07:52:50Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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