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Equality of Dedekind sums modulo $8 \mathbb {Z}$

Volume 170 / 2015

Emmanuel Tsukerman Acta Arithmetica 170 (2015), 67-72 MSC: Primary 11F20. DOI: 10.4064/aa170-1-5

Abstract

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 $8\mathbb {Z}$. These yield new necessary conditions for equality of two Dedekind sums. In addition, we resolve a conjecture of Girstmair [arXiv:1501.00655].

Authors

  • Emmanuel TsukermanDepartment of Mathematics
    University of California
    Berkeley, CA 94720-3840, U.S.A.
    e-mail

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