2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75061We 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.Long but Ready to be UnderstoodNumber TheoryAlgebraic Geometrytext