vix.ing · top · new · best · stats · spec

The number of Dedekind sums with equal fractional parts

2013/09/17 by Kurt Girstmair, Girstmair, Kurt
Mathematics · #11F40 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT) #math.NT #msc:11F40

paper · pdf · doi:10.48550/arxiv.1309.4226

7 pages

openalex publication_date 2013/09/17 · arxiv created 2013/10/22 · arxiv updated 2013/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a previous it was shown that the Dedkind sums 12s(m,n) and 12s(x,n), 1≤ m,x≤ n, (m,n)=(x,n)=1, are equal mod \Z if, and only if, (x-m)(xm-1)≡ 0 mod n. Here we determine the cardinality of numbers x in the above range that satisfy this congruence for a given number m.

Related