P-adic Rankin-Selberg L-functions in universal deformation families and functional equations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908645775638528 |
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| author | Hao, Zeping Loeffler, David |
| author_facet | Hao, Zeping Loeffler, David |
| contents | We construct a $p$-adic Rankin-Selberg $L$-function associated to the product of two families of modular forms, where the first is an ordinary (Hida) family, and the second an arbitrary universal-deformation family (without any ordinarity condition at $p$). This gives a function on a 4-dimensional base space - strictly larger than the ordinary eigenvariety, which is 3-dimensional in this case. We prove our $p$-adic $L$-function interpolates all critical values of the Rankin-Selberg $L$-functions for the classical specialisations of our family, and derive a functional equation for our $p$-adic $L$-function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12611 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | P-adic Rankin-Selberg L-functions in universal deformation families and functional equations Hao, Zeping Loeffler, David Number Theory 11F67, 11F80, 11R23 We construct a $p$-adic Rankin-Selberg $L$-function associated to the product of two families of modular forms, where the first is an ordinary (Hida) family, and the second an arbitrary universal-deformation family (without any ordinarity condition at $p$). This gives a function on a 4-dimensional base space - strictly larger than the ordinary eigenvariety, which is 3-dimensional in this case. We prove our $p$-adic $L$-function interpolates all critical values of the Rankin-Selberg $L$-functions for the classical specialisations of our family, and derive a functional equation for our $p$-adic $L$-function. |
| title | P-adic Rankin-Selberg L-functions in universal deformation families and functional equations |
| topic | Number Theory 11F67, 11F80, 11R23 |
| url | https://arxiv.org/abs/2405.12611 |