Derivatives of Dedekind sums and their reciprocity law.
type: Item
instance of: scholarly article
title: Derivatives of Dedekind sums and their reciprocity law.
zbMATH Open document ID: 1038.11028
DOI: 10.1016/S0022-314X(02)00046-X
author: Kaori Ota
published in: Journal of Number Theory
publication date: 2003-04-28T00:00:00Z
review text: The author evaluates Barnes' double zeta function at the negative integers in two ways, one in terms of Bernoulli numbers, and another as a finite sum of Hurwitz zeta functions. Equating these expressions leads to a new and interesting proof of the reviewer's reciprocity law for generalized Dedekind sums. More general results are indicated as being obtainable from Barnes' multiple zeta functions.
Mathematics Subject Classification ID: 11F20
Mathematics Subject Classification ID: 11B68
Mathematics Subject Classification ID: 11M41
zbMATH DE Number: 1902880
zbMATH Keywords: Derivatives of Dedekind sums
zbMATH Keywords: reciprocity law
zbMATH Keywords: Barnes' multiple zeta function
zbMATH Keywords: Stirling modular form
zbMATH Keywords: double gamma function
reviewed by: Tom M. Apostol
MaRDI profile type: Publication
cites work: Generalized Dedekind sums and transformation formulae of certain Lambert series
cites work: Reciprocity laws for generalized higher dimensional Dedekind sums
cites work: Q4519882
cites work: Reciprocity formulae for general Dedekind-Rademacher sums
cites work: Berechnung der Werte von Zetafunktionen totalreeller kubischer Zahlkörper an ganzzahligen Stellen mittels verallgemeinerter Dedekindscher Summen. I.
cites work: Q1098885
cites work: Properties of higher-dimensional Shintani generating functions and cocycles on \(\text{PGL}_ 3(\mathbb{Q})\).
cites work: On the multiple gamma-functions
cites work: Generalizations of Dedekind sums and their reciprocity laws
cites work: Q5666618
cites work: Q4138810
cites work: A proof of the classical Kronecker limit formula
cites work: Q3840745
cites work: Higher dimensional Dedekind sums
description: scientific article; zbMATH DE number 1902880