Seminar in Algebraic Geometry and Number Theory

Abstract: We examine the moments of the number of lattice points in a fixed ball of volume V for lattices in Euclidean space which are modules over the ring of integers O of a number field K. In particular, we show that moments obtained for “lifts of codes” to O-modules converge to the Rogers integral formula for the space of free O-module lattices. This extends work of Rogers for Z-lattices.

Joint work with Maryna Viazovska, Nihar Gargava and Vlad Serban.