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On the value of the Dedekind sum

Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1987
This paper studies the nth Dedekind sum (which involves powers of the greatest integer function). For \(n=2,3\), the author gives, by elementary methods, recursive formulas which could be used to evaluate these sums.
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On the values of the Dedekind sum

Mathematische Zeitschrift, 1985
Let \(S(h,k)\) be the Dedekind sum. We define \(t(h,k)=6k\, s(h,k)\). It is known that \(t(h,k)\) is an integer for all \(h\) and \(k\). The problem we address is that of characterizing, for a given integer \(t\), all pairs \((h,k)\) such that \(t(h,k)=t\).
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On the general Dedekind sums and two-term exponential sums. [PDF]

ScientificWorldJournal, 2014
Zhang J, Zhang W.
europepmc   +1 more source

p-adic vertex operator algebras. [PDF]

Res Number Theory, 2023
Franc C, Mason G.
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On generalized Dedekind sums

Journal of Number Theory, 1979
The sums in question were introduced by \textit{L. Carlitz} [Math. Z. 85, 83--90 (1964; Zbl 0122.05104)] and are defined by \[ s_r(a,b\mid x,y) = \sum_{j=0}^{\vert b\vert - 1} P_r\left(\frac{a(j+y)}{b} + x\right) P_1\left(\frac{j+y}{b}\right) \] where \(r, a, b\) are integers, \(r\ge 0\), \(b\ne 0\), and \(x, y\) are real.
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A hybrid mean value involving Dedekind sums and the general exponential sums. [PDF]

ScientificWorldJournal, 2014
Li J, Wang T.
europepmc   +1 more source

Bits and pieces: understanding information decomposition from part-whole relationships and formal logic. [PDF]

Proc Math Phys Eng Sci, 2021
Gutknecht AJ, Wibral M, Makkeh A.
europepmc   +1 more source

Process and Time. [PDF]

Entropy (Basel), 2023
Sulis W.
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Fast computation of generalized dedekind sums

International Journal of Number Theory
We construct an algorithm that reduces the complexity for computing generalized Dedekind sums from exponential to polynomial time. We do so by using an efficient word rewriting process in group theory.
Preston Tranbarger, Jessica Wang
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Decomposing past and future: Integrated information decomposition based on shared probability mass exclusions. [PDF]

PLoS One, 2023
Varley TF.
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