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December 2016 Counting lattice points in certain rational polytopes and generalized Dedekind sums
Kazuhito Kozuka
Funct. Approx. Comment. Math. 55(2): 199-214 (December 2016). DOI: 10.7169/facm/2016.55.2.4

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.

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Kazuhito Kozuka. "Counting lattice points in certain rational polytopes and generalized Dedekind sums." Funct. Approx. Comment. Math. 55 (2) 199 - 214, December 2016. https://doi.org/10.7169/facm/2016.55.2.4

Information

Published: December 2016
First available in Project Euclid: 17 December 2016

zbMATH: 1384.05028
MathSciNet: MR3584568
Digital Object Identifier: 10.7169/facm/2016.55.2.4

Subjects:
Primary: 05A15
Secondary: 11F20

Rights: Copyright © 2016 Adam Mickiewicz University

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Vol.55 • No. 2 • December 2016
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