Formal duality and generalizations of the Poisson summation formula
arXiv:1306.6796 · doi:10.1090/conm/625/12495
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