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arXiv · 2305.07707

On $p$-adic $L$-functions for $\text{GSp}_4 \times \text{GL}_2$

David Loeffler·Óscar Rivero
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Abstract

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.

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David Loeffler, Óscar Rivero. 2025-04-14. On $p$-adic $L$-functions for $\text{GSp}_4 \times \text{GL}_2$. https://doi.org/10.2140/pjm.2025.335.373

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