  We first study geometrically oriented truncation associated with stability
along the line of Arthur's analytic truncation. Then, we give a detailed
discussion on the so-called Abelian Parts of non-abelian L functions, using an
advanced version of Rankin-Selberg method. All this is based on
Jacquet-Lapid-Rogawski's regularized integrals over cones.
  This is an integrated part of our Program for Geometric Arithmetic.
