Geodesic
Equality of Dedekind sums modulo $8 \mathbb {Z}$
Emmanuel Tsukerman1
1 Department of Mathematics University of California Berkeley, CA 94720-3840, U.S.A.
Acta Arithmetica, Tome 170 (2015) no. 1, pp. 67-72

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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 $8\mathbb {Z}$. These yield new necessary conditions for equality of two Dedekind sums. In addition, we resolve a conjecture of Girstmair [arXiv:1501.00655].
DOI : 10.4064/aa170-1-5
Keywords: using generalization due lerch bull int acad fran ois joseph classical lemma zolotarev employed zolotarevs proof law quadratic reciprocity determine necessary sufficient conditions difference dedekind sums mathbb these yield necessary conditions equality dedekind sums addition resolve conjecture girstmair arxiv

Emmanuel Tsukerman 1

1 Department of Mathematics University of California Berkeley, CA 94720-3840, U.S.A. 
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Emmanuel Tsukerman. Equality of Dedekind sums modulo $8 \mathbb {Z}$. Acta Arithmetica, Tome 170 (2015) no. 1, pp. 67-72. doi: 10.4064/aa170-1-5

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