## Functiones et Approximatio Commentarii Mathematici

### Counting lattice points in certain rational polytopes and generalized Dedekind sums

Kazuhito Kozuka

#### 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

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

#### 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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