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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 inthe $H^2$ of Shimura varieties for $\text{GSp}_4$, in this note we explore theinterpolation of classes in the $H^1$, which allows us to access to a differentrange of weights. Further, we show an interpolation property in terms ofcomplex $L$-values using the algebraicity results established in previous workby the authors.

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