Theorems of Brion, Lawrence, and Varchenko on rational generating functions for cones

We discuss and give elementary proofs of results of Brion and of nLawrence-Varchenko on the lattice-point enumerator generating functions for npolytopes and cones. This largely expository note contains a new proof of nBrion s Formula using irrational decompositions, and a generalization of the nLawrence-Varchenko formula.