Exceptional values of the Dedekind symbol
type: Item
instance of: scholarly article
title: Exceptional values of the Dedekind symbol
zbMATH Open document ID: 0595.10009
DOI: 10.1016/0022-314X(86)90100-9
author: Chiaki Nagasaka
published in: Journal of Number Theory
publication date: 1986-01-01T00:00:00Z
review text: For coprime integers h and k with \(k>0\), the Dedekind symbol (h,k) is defined as \[ (h,k)=6k\sum^{k-1}_{r=1}(r/k)(hr/k-[hr/k]-). \] For \(w\equiv 0,\pm 1,\pm 3 (mod 9)\) the order of w is defined by ord w\(=\inf \{k|\) \((h,k)=w\) for some \(h\}\) ; if w does not occur as a value (h,k) then ord w\(=\infty\) and w is called an exceptional value. The author describes numerical work that strongly suggests the following conjecture: w is exceptional if and only if (i) w-1 is a square not divisible by any prime \(\equiv \pm 3 (mod 8)\) or (ii) \(w=12\), 44, 107, 152 or 172.
Mathematics Subject Classification ID: 11B39
zbMATH DE Number: 3957205
zbMATH Keywords: Dedekind sum
zbMATH Keywords: Dedekind symbol
zbMATH Keywords: exceptional value
reviewed by: Kenneth S. Williams
MaRDI profile type: Publication
cites work: Some arithmetic on Dedekind sums
cites work: Q4775913
cites work: On the theory of Dedekind sums.
cites work: Q5663963
cites work: Zum Wertevorrat der Dedekindschen Summen
description: scientific article; zbMATH DE number 3957205