Functiones et Approximatio Commentarii Mathematici

Counting lattice points in certain rational polytopes and generalized Dedekind sums

Kazuhito Kozuka

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Let ${\mathcal P} \subset {\mathbf R}^n$ be a rational convex polytope with vertices at the origin and on each positive coordinate axes. On the basis of the study on counting lattice points in $t{\mathcal P}$ with positive integer $t$, which is deeply connected with reciprocity laws for generalized Dedekind sums, we study the number of lattice points in the shifted polytope of $t{\cal P}$ by a fixed rational point. Certain generalized multiple Dedekind sums appear naturally in the main result.

Article information

Funct. Approx. Comment. Math., Volume 55, Number 2 (2016), 199-214.

First available in Project Euclid: 17 December 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]
Secondary: 11F20: Dedekind eta function, Dedekind sums

rational polytopes lattice points Ehrhart quasipolynomial


Kozuka, Kazuhito. Counting lattice points in certain rational polytopes and generalized Dedekind sums. Funct. Approx. Comment. Math. 55 (2016), no. 2, 199--214. doi:10.7169/facm/2016.55.2.4.

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