On the Geometric Side of the Arthur Trace Formula for the Symplectic Group of Rank 2

The authors study the non-semisimple terms in the geometric side of the Arthur trace formula for the split symplectic similitude group and the split symplectic group of rank $2$ over any algebraic number field. In particular, they express the global coefficients of unipotent orbital integrals in terms of Dedekind zeta functions, Hecke $L$-functions, and the Shintani zeta function for the space of binary quadratic forms.