A reciprocity theorem and a three-term relation for generalized Dedekind-Rademacher sums
L. Carlitz (1980)
Acta Arithmetica
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L. Carlitz (1980)
Acta Arithmetica
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Yumiko Nagasaka, Kaori Ota, Chizuru Sekine (2003)
Acta Arithmetica
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Emmanuel Tsukerman (2015)
Acta Arithmetica
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Using a generalization due to Lerch [Bull. Int. Acad. François Joseph 3 (1896)] of a classical lemma of Zolotarev, employed in Zolotarev's proof of the law of quadratic reciprocity, we determine necessary and sufficient conditions for the difference of two Dedekind sums to be in 8ℤ. These yield new necessary conditions for equality of two Dedekind sums. In addition, we resolve a conjecture of Girstmair [arXiv:1501.00655].
Abdelmejid Bayad, Abdelaziz Raouj (2010)
Acta Arithmetica
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Matthias Beck, Anastasia Chavez (2011)
Acta Arithmetica
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Wenpeng Zhang (2003)
Acta Arithmetica
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Kurt Girstmair (2003)
Acta Arithmetica
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L. Carlitz (1964)
Mathematische Zeitschrift
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Matthias Beck (2003)
Acta Arithmetica
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L. Carlitz (1976)
Acta Arithmetica
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Michael Atiyah (1987)
Mathematische Annalen
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G. Myerson (1985)
Mathematische Zeitschrift
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Nicolae Dăneţ (2011)
Banach Center Publications
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The aim of this paper is to show that every Hausdorff continuous interval-valued function on a completely regular topological space X corresponds to a Dedekind cut in C(X) and conversely.
Kazuhito Kozuka (2011)
Acta Arithmetica
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