Denis Charles (UW-Madison): Counting Lattice Vectors (Continued from talk on 3/11/2002)

We consider the problem of exactly counting the number of lattice vectors of a given norm (L_2). We show that this problem is #P - complete, and give an interesting deterministic exponential time algorithm for this problem using Modular forms. This is work in progress, and no knowledge of modular forms will be assumed in the presentation.