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.
Citation
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
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