Generalizing Lattice Point Enumeration
Thomas Kunze
Department of Mathematics
Faculty Supervisor: Matthias Beck
Given a d-dimensional convex polytope Q with integer vertices, the number of lattice points contained in the dilation nQ is a polynomial in n, for n a positive integer. We generalize this result by fixing a linear form subject to certain conditions and considering certain weighted sums encoding the output of the linear form at the lattice points contained in Q. These sums are the output of a certain polynomial using two variables. We prove certain statements in the context of this generalization and expand on known results.