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Formal duality and generalizations of the Poisson summation formula (1306.6796v2)
Published 28 Jun 2013 in math.NT and math.MG
Abstract: We study the notion of formal duality introduced by Cohn, Kumar, and Sch\"urmann 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.
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