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A Certain Generalized Dedekind Sum
Tokyo Journal of Mathematics, 1987 The author defines two generalizations of the classical Dedekind sums which involve powers of roots of unity and the greatest integer function. (These are also analogues of sums studied by \textit{L. Carlitz} [Fibonacci Q. 15, 78-84 (1977; Zbl 0362.10004)].) His goal is to evaluate these sums and give reciprocity relations for them.
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Acta Arithmetica, 1987 This paper collects together a number of results concerning the classical Dedekind sum and the so-called Hardy sums which are of a similar character. One of the many results stated in the paper gives simple explicit formulas for the Hardy sums in terms of Dedekind sums.
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Integer-valued polynomials on valuation rings of global fields with prescribed lengths of factorizations. [PDF]
Mon Hefte Math, 2023 Fadinger-Held V, Frisch S, Windisch D.
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Cotangent sums, a further generalization of Dedekind sums
Journal of Number Theory, 1984 Let \(\cot(z)=\cot \pi z\) if \(z\neq\) integer, \(\cot(z)=0\) otherwise. The cotangent sums considered here are \[ (1/c)\sum_{\nu mod c}\cot(- x+a(\nu +z)/c) \cot(-y+b(\nu +z)/c) \] where a,b,c are positive integers coprime in pairs, and x,y,z are real numbers in the interval [0,1). The author derives a three-term relation which, in the special case \(
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A note on hardy type sums and Dedekind sums
Filomat, 2016 In [9], Cetin et al. defined a new special finite sum which is denoted by C1(h,k). In this paper, with the help of two-term polynomial relation, we will give the explicit values of the sum C1(h,k). We will see that for the odd values of h and k, this sum only depends on one variable.
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On the infinite Borwein product raised to a positive real power. [PDF]
Ramanujan J, 2023 Schlosser MJ, Zhou NH.
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Journal of Number Theory, 1977 AbstractA necessary and sufficient condition is given for a positive integer to appear as the denominator of some reduced Dedekind sum.
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From Magnitudes to Geometry and Back: De Zolt's Postulate. [PDF]
Theoria, 2022 Giovannini EN, Lassalle-Casanave A.
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Hyperseries in the non-Archimedean ring of Colombeau generalized numbers. [PDF]
Mon Hefte Math, 2022 Tiwari D, Giordano P.
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