Equality of Dedekind sums mod $8 \mathbb{Z}$
Number Theory
2015-01-22 v2
Abstract
Using a generalization due to Lerch [M. Lerch, Sur un th\'{e}or\`{e}me de Zolotarev. Bull. Intern. de l'Acad. Fran\c{c}ois Joseph 3 (1896), 34-37] 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 . These yield new necessary conditions for equality of two Dedekind sums. In addition, we resolve a conjecture of Girstmair [Girstmair, Congruences mod 4 for the alternating sum of the partial quotients, arXiv: 1501.00655].
Cite
@article{arxiv.1501.03544,
title = {Equality of Dedekind sums mod $8 \mathbb{Z}$},
author = {Emmanuel Tsukerman},
journal= {arXiv preprint arXiv:1501.03544},
year = {2015}
}