Results 71 to 80 of about 12,032 (167)
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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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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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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Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums. [PDF]
Math Ann, 2023 Minelli P, Sourmelidis A, Technau M.
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Modular knots, automorphic forms, and the Rademacher symbols for triangle groups. [PDF]
Res Math Sci, 2023 Matsusaka T, Ueki J.
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Tracking the Photomineralization Mechanism in Irradiated Lab-Generated and Field-Collected Brown Carbon Samples and Its Effect on Cloud Condensation Nuclei Abilities. [PDF]
ACS Environ Au, 2023 Müller S, Giorio C, Borduas-Dedekind N.
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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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On the arithmetic of stable domains. [PDF]
Commun Algebra, 2021 Bashir A, Geroldinger A, Reinhart A.
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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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