Functiones et Approximatio Commentarii Mathematici

Counting lattice points in certain rational polytopes and generalized Dedekind sums

Kazuhito Kozuka

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Abstract

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

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

Dates
First available in Project Euclid: 17 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.facm/1481943882

Digital Object Identifier
doi:10.7169/facm/2016.55.2.4

Mathematical Reviews number (MathSciNet)
MR3584568

Zentralblatt MATH identifier
1384.05028

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

Keywords
rational polytopes lattice points Ehrhart quasipolynomial

Citation

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. https://projecteuclid.org/euclid.facm/1481943882


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