On the reciprocity formula for generalized Dedekind sums
type: Item
instance of: scholarly article
title: On the reciprocity formula for generalized Dedekind sums
zbMATH Open document ID: 0685.10009
author: Yugen Takegahara
published in: Hokkaido Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: The sums in the title are defined by \[ s(h,k,r)=\sum^{k}_{j=1}((j/k))((hj+r/k)), \] where h and k are integers, \(k>0\), r is a real number, \(((x))=x-[x]\) if \(x\neq integer\), and \(((x))=0\) otherwise. The author gives a new proof of the reciprocity law for these sums. He also relates these sums to a function introduced by \textit{T. Yoshida} [J. Algebra 118, No.2, 498-527 (1988; Zbl 0656.20008)] on a finite abelian group.
Mathematics Subject Classification ID: 11B39
zbMATH DE Number: 4122054
zbMATH Keywords: generalized Dedekind sums
zbMATH Keywords: reciprocity law
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1381517732
OpenAlex ID: W1988027342
DOI: 10.14492/HOKMJ/1381517732
description: scientific article; zbMATH DE number 4122054