volume 27, issue 4, P443-459 2002
DOI: 10.1007/s00454-001-0082-3
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## Abstract: Abstract. We give explicit, polynomial-time computable formulas for the number of integer points in any twodimensional 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 …

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