Equality of Dedekind sums modulo $8 \mathbb {Z}$
Volume 170 / 2015
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].
