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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.
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