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

Abstract

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 B\"ocherer conjecture for the central $L$-values with anticyclotomic twists.