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].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa170-1-5,
author = {Emmanuel Tsukerman},
title = {Equality of Dedekind sums modulo 8$\mathbb{Z}$},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {67-72},
zbl = {06459958},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa170-1-5}
}
Emmanuel Tsukerman. Equality of Dedekind sums modulo 8ℤ. Acta Arithmetica, Tome 168 (2015) pp. 67-72. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa170-1-5/