Generalized Dedekind sums.
L. Carlitz (1964)
Mathematische Zeitschrift
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L. Carlitz (1964)
Mathematische Zeitschrift
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F.M. Ragab, T.M. MacRobert (1962)
Mathematische Zeitschrift
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K.S. Rao (1936)
Mathematische Zeitschrift
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K.S. Rao (1935)
Mathematische Zeitschrift
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I. Chowla (1936)
Mathematische Zeitschrift
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Roelof W. Bruggemen (1989)
Mathematische Zeitschrift
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A. Oppenheim (1934)
Mathematische Zeitschrift
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Daniel B. Shapiro, Enzo R. Gentile (1978)
Mathematische Zeitschrift
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Murray Marshall (1974)
Mathematische Zeitschrift
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Robert Sczech (1994)
Mathematische Annalen
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Kurt Girstmair (2003)
Acta Arithmetica
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H.O. Foulkes (1956)
Mathematische Zeitschrift
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H.F. Blichfeldt (1935)
Mathematische Zeitschrift
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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].