Explicit and efficient formulas for the lattice point count in rational polygons using Dedekind-Rademacher sums

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dc.creatorBeck, Matthias
dc.creatorRobins, Sinai
dc.date2001-11-30
dc.date2003-06-04
dc.date.accessioned2026-07-07T04:44:54Z
dc.date.available2026-07-07T04:44:54Z
dc.descriptionWe give explicit, polynomial-time computable formulas for the number of integer points in any two-dimensional rational polygon. A rational polygon is one whose vertices have rational coordinates. We find that the basic building blocks of our formulas are Dedekind-Rademacher sums, which are polynomial-time computable finite Fourier series. As a by-product we rederive a reciprocity law for these sums due to Gessel, which generalizes the reciprocity law for the classical Dedekind sums. In addition, our approach shows that Gessel's reciprocity law is a special case of the one for Dedekind-Rademacher sums, due to Rademacher.
dc.description16 pages, updated journal reference
dc.identifierhttps://arxiv.org/abs/math/0111329
dc.identifierhttp://arxiv.org/abs/math/0111329
dc.identifierDiscrete & Comp. Geom. 27 (2002), 443--459
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62781
dc.subjectCombinatorics
dc.subjectNumber Theory
dc.subject05A15, 52C05, 11H06, 11L03
dc.titleExplicit and efficient formulas for the lattice point count in rational polygons using Dedekind-Rademacher sums
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