Results 81 to 90 of about 12,032 (167)

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 infinite Borwein product raised to a positive real power. [PDF]

Ramanujan J, 2023
Schlosser MJ, Zhou NH.
europepmc   +1 more source

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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The volumes of Miyauchi subgroups. [PDF]

Arch Math, 2022
Lesesvre D, Petrow I.
europepmc   +1 more source

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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From Magnitudes to Geometry and Back: De Zolt's Postulate. [PDF]

Theoria, 2022
Giovannini EN, Lassalle-Casanave A.
europepmc   +1 more source

Trace Metals in Global Air: First Results from the GAPS and GAPS Megacities Networks. [PDF]

Environ Sci Technol, 2023
Mastin J, Saini A, Schuster JK, Harner T, Dabek-Zlotorzynska E, Celo V, Gaga EO.   +6 more
europepmc   +1 more source

Revealing the Dynamics of Neural Information Processing with Multivariate Information Decomposition. [PDF]

Entropy (Basel), 2022
Newman EL, Varley TF, Parakkattu VK, Sherrill SP, Beggs JM.   +4 more
europepmc   +1 more source

p-adic Dedekind sums

The goal of this paper is to define p-adic Dedekind sums. The basic idea is to use the p-adic interpolation of certain partial zeta functions to interpolate the higher-order Dedekind sums introduced by \textit{T. M. Apostol} [Duke Math. J. 17, 147-157 (1950; Zbl 0039.038)]. The reciprocity law for higher-order Dedekind sums leads, via interpolation, to
Rosen, Kenneth H., Snyder, William M.
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Steps Toward a Philosophy for Mathematicians. [PDF]

Math Intell, 2023
Fenstad JE.
europepmc   +1 more source