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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2305.07707 |
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| _version_ | 1866908360920530944 |
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| author | Loeffler, David Rivero, Óscar |
| author_facet | Loeffler, David Rivero, Óscar |
| contents | We use higher Coleman theory to construct a new $p$-adic $L$-function for $\text{GSp}_4 \times \text{GL}_2$. While previous works by the first author, Pilloni, Skinner and Zerbes had considered the $p$-adic variation of classes in the $H^2$ of Shimura varieties for $\text{GSp}_4$, in this note we explore the interpolation of classes in the $H^1$, which allows us to access to a different range of weights. Further, we show an interpolation property in terms of complex $L$-values using the algebraicity results established in previous work by the authors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_07707 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On $p$-adic $L$-functions for $\text{GSp}_4 \times \text{GL}_2$ Loeffler, David Rivero, Óscar Number Theory We use higher Coleman theory to construct a new $p$-adic $L$-function for $\text{GSp}_4 \times \text{GL}_2$. While previous works by the first author, Pilloni, Skinner and Zerbes had considered the $p$-adic variation of classes in the $H^2$ of Shimura varieties for $\text{GSp}_4$, in this note we explore the interpolation of classes in the $H^1$, which allows us to access to a different range of weights. Further, we show an interpolation property in terms of complex $L$-values using the algebraicity results established in previous work by the authors. |
| title | On $p$-adic $L$-functions for $\text{GSp}_4 \times \text{GL}_2$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2305.07707 |