Affiliation:
1. Institut für Mathematik, Universität Innsbruck, Technikerstr. 13/7, A-6020 Innsbruck, Austria
Abstract
In [Jabuka, Robins and Wang, When are two Dedekind sums equal? Internat. J. Number Theory7 (2011) 2197–2202], it was shown that the Dedekind sums s(m1, n) and s(m2, n) are equal only if (m1m2-1)(m1-m2) ≡ 0 mod n. Here we show that the latter condition is equivalent to 12s(m1, n) - 12s(m2, n) ∈ ℤ. In addition, we determine, for a given number m1, the number of integers m2in the range 0 ≤ m2< n, (m1, m2) = 1, such that 12s(m1, n) - 12s(m2, n) ∈ ℤ, provided that n is square-free.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
8 articles.
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1. Note on the index conjecture in zero-sum theory and its connection to a Dedekind-type sum;Journal of Number Theory;2016-11
2. Fractional parts of Dedekind sums;International Journal of Number Theory;2016-05-10
3. On Dedekind sums with equal values;International Journal of Number Theory;2016-02-18
4. Dedekind sums s(a, b) and inversions modulo b;International Journal of Number Theory;2015-11-05
5. Equality of Dedekind sums mod ℤ, 2ℤ and 4ℤ;International Journal of Number Theory;2015-08-26