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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2512.01184 |
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| _version_ | 1866911306002464768 |
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| author | Gu, Haonan |
| author_facet | Gu, Haonan |
| contents | This article studies the finite--slope analogue of Loeffler's conjectural framework for Rankin--Selberg $p$-adic $L$-functions in universal deformation families. Starting from residual representations $\barρ_1,\barρ_2$ of tame level~$1$ satisfying Hypothesis~3.1 of~\cite{LoefflerUD}, we consider the half--ordinary Panchishkin family $(R,V,V^+)$ of Example~3.17 of loc.\ cit., where the first factor varies in the ordinary Hida deformation and the second factor in the unrestricted universal deformation space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01184 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards a finite-slope universal Rankin-Selberg p-adic L-function Gu, Haonan Number Theory This article studies the finite--slope analogue of Loeffler's conjectural framework for Rankin--Selberg $p$-adic $L$-functions in universal deformation families. Starting from residual representations $\barρ_1,\barρ_2$ of tame level~$1$ satisfying Hypothesis~3.1 of~\cite{LoefflerUD}, we consider the half--ordinary Panchishkin family $(R,V,V^+)$ of Example~3.17 of loc.\ cit., where the first factor varies in the ordinary Hida deformation and the second factor in the unrestricted universal deformation space. |
| title | Towards a finite-slope universal Rankin-Selberg p-adic L-function |
| topic | Number Theory |
| url | https://arxiv.org/abs/2512.01184 |