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GENERALIZED SOLID-ANGLE THEORY FOR REAL POLYTOPES (2011)

Desario, D., Robins, S.

Oxford University Press

In: Quarterly Journal of Mathematics

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Publication Date: 2011-11-24

Description: We extend some theorems from the context of solid-angle sums over rational polytopes to the context of solid-angle sums over real polytopes. Moreover, we also consider any real dilation parameter, as opposed to the traditional integer dilation parameters. One of the main results is an extension of Macdonald's solid-angle quasi-polynomial for rational polytopes to a real analytic function of the dilation parameter, for any real convex polytope. Consequently, we find an extension of Macdonald's reciprocity law for real dilation parameters, over real polytopes.

Print ISSN: 0033-5606

Electronic ISSN: 1464-3847

Topics: Mathematics

Published by Oxford University Press

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