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arXiv · 1306.6796

Formal duality and generalizations of the Poisson summation formula

Henry Cohn·Abhinav Kumar·Christian Reiher·Achill Schürmann
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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.

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Henry Cohn, Abhinav Kumar, Christian Reiher, Achill Schürmann. 2016-11-27. Formal duality and generalizations of the Poisson summation formula. https://doi.org/10.1090/conm%2F625%2F12495

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