Some numerical computations concerning spinor zeta functions in genus $\boldsymbol{2}$ at the central point

Abstract

We numerically compute the central critical values of odd quadratic character twists with respect to some small discriminants D of spinor zeta functions attached to Seigel-Hecke eigenforms F of genus 2 in the first few cases where F does not belong to the Maass space. As a result, in the cases considered we can numerically confirm a conjecture of Bocherer, according to which these central critical values should be proportional to the squares of certain finite sums of Fourier coefficients of F.