Theorems of Brion, Lawrence, and Varchenko on rational generating   functions for cones
  We discuss and give elementary proofs of results of Brion and of Lawrence-Varchenko on the lattice-point enumerator generating functions for polytopes and cones. This largely expository note contains a new proof of Brion's Formula using irrational decompositions, and a generalization of the Lawrence-Varchenko formula. 
Matthias Beck, Christian Haase, and Frank Sottile