Equality of Dedekind sums mod $\mathbb{Z},2\mathbb{Z}$ and $4\mathbb{Z}$

Emmanuel Tsukerman

doi:10.1142/S1793042115500748

paper

Equality of Dedekind sums mod $Z, 2 Z$ and $4 Z$

arXiv:1408.3225 · doi:10.1142/S1793042115500748

Abstract

In [Girstmair, A criterion for the equality of Dedekind sums mod $Z$ , Internat. J. Number Theory 10: (2014) 565--568], it was shown that the necessary condition $b ∣ (a_{1} a_{2} - 1) (a_{1} - a_{2})$ for equality of two dedekind sums $s (a_{1}, b)$ and $s (a_{2}, b)$ given in [Jabuka, Robins and Wang, When are two Dedekind sums equal? Internat. J. Number Theory 7: (2011) 2197--2202] is equivalent to $12 s (a_{1}, b) - 12 s (a_{2}, b) \in Z$ . In this note, we give a new proof of this result and then find two additional necessary and sufficient conditions for $12 s (a_{1}, b) - 12 s (a_{2}, b) \in 2 Z, 4 Z$ . These give new necessary conditions on equality of Dedekind sums.

3 pages

Equality of Dedekind sums mod Z,2Z and 4Z

Abstract

Equality of Dedekind sums mod $Z, 2 Z$ and $4 Z$