Arthur's Periods, Regularized Integrals and Refined Structures of   Non-Abelian L-Functions
  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. 
Lin Weng