Maximal parabolic terms in the Selberg trace formula for SL(3, Z)⧹SL(3, R)/SO(3, R)

AbstractIn this paper we study the contribution to the Selberg trace formula for SL(3, Z)⧹SL(3, R)/SO(3, R) of orbital integrals coming from regular elements of a maximal parabolic subgroup of SL(3, Z). Because the contribution is not convergent the integrals are truncated in the standard way and the rate of divergence is calculated. We show that these orbital integrals are reduced to orbital integrals of a slightly different function for hyperbolic elements coming from SL(3, Z) intersected with a rank one subgroup of SL(3, R)