Formal duality and generalizations of the Poisson summation formula

Abstract

We study the notion of formal duality introduced by Cohn, Kumar, and Schürmann in their computational study of energy-minimizing particle configurations in Euclidean space. In particular, using the Poisson summation formula we reformulate formal duality as a combinatorial phenomenon in finite abelian groups. We give new examples related to Gauss sums and make some progress towards classifying formally dual configurations.

18 pages

References in corpus (2)

• Ground states and formal duality relations in the Gaussian core model
• Counterintuitive ground states in soft-core models

Cited by in corpus (2)

• The isospectral problem for flat tori from three perspectives
• Formal-dual subsets of cyclic groups of prime power order