Anticyclotomic p-adic spinor L-functions for PGSp(4)

The Boecherer conjecture is a generalization of the Waldspurger formula and relates squares of Bessel periods
of genus two Siegel cusp forms to the central L-values.
This conjecture was currently proved by Furusawa and Morimoto for the special Bessel period, and the general
case is a work-in-progress. In this talk I will construct a square root of an anticyclotomic p-adic L-function with
explicit interpolation formulas for Siegel cusp forms of genus 2 and scalar weight greater than 1 with respect to
paramodular groups of square-free level, assuming the Boecherer conjecture for the L-values with anticyclotomic twist.
This is a joint work with Ming-Lun Hsieh.