Bessel periods and anticyclotomic $p$-adic spinor $L$-functions

We construct the anticyclotomic $p$-adic $L$-function that interpolates a square root of central values of twisted spinor $L$-functions of a quadratic base change of a Siegel cusp form of genus $2$ with respect to a paramodular group of square-free level, assuming the Böcherer conjecture for the central $L$-values with anticyclotomic twists.

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