A Polynomial Time Algorithm for Calculating Fourier-Dedekind Sums

We solve an open problem proposed in the book "Computing the continuous discretely" written by Matthias Beck and Sinai Robins. That is, we provide a practical polynomial time algorithm for calculating Fourier-Dedekind sums. The algorithm is simple modular Barvinok's simplicial cone de...

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Veröffentlicht in:Experimental mathematics Jg. 34; H. 3; S. 342 - 349
Hauptverfasser: Xin, Guoce, Xu, Xinyu
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Taylor & Francis 03.07.2025
Schlagworte:
Barvinok's algorithm
constant terms
Dedekind sum
Fourier-Dedekind sum
Primary: 11F20
Secondary: 11Y16
ISSN:1058-6458, 1944-950X
Online-Zugang:Volltext
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Zusammenfassung:We solve an open problem proposed in the book "Computing the continuous discretely" written by Matthias Beck and Sinai Robins. That is, we provide a practical polynomial time algorithm for calculating Fourier-Dedekind sums. The algorithm is simple modular Barvinok's simplicial cone decomposition. It can be easily adapted into De Leora et al.'s LattE package, which gives a nice implementation of Barvinok's polynomial time algorithm.
ISSN:1058-6458
1944-950X
DOI:10.1080/10586458.2024.2364264