Moment estimates of module lattice points for effective lattice constructions

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 of a number field $K$. In particular, we show that moments obtained for “lifts of codes” to $\mathcal{O}_K$-modules converge to the Rogers integral formula for the space of free $\mathcal{O}_K$-module lattices. This extends work of Rogers for $\mathbb{Z}$-lattices. Joint work with Maryna Viazovska, Nihar Gargava and Vlad Serban.

number theory

Audience: researchers in the topic

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London number theory seminar

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