Magnification relations in gravitational lensing via multidimensional   residue integrals
  We investigate the so-called magnification relations of gravitational lensing models. We show that multidimensional residue integrals provide a simple explanation for the existence of these relations, and an effective method of computation. We illustrate the method with several examples, thereby deriving new magnification relations for galaxy lens models and microlensing (point mass lensing). 
Neal Dalal and Jeffrey M. Rabin