Dedekind symbols with plus reciprocity laws
type: Item
instance of: scholarly article
title: Dedekind symbols with plus reciprocity laws
zbMATH Open document ID: 1188.11014
author: Shinji Fukuhara
published in: Journal of Number Theory
publication date: 2008-12-05T00:00:00Z
review text: Certain generalizations of the classical Dedekind sums are studied in this paper. These generalizations are called Dedekind symbols and they are defined as complex valued functions on visible points in the right half plane. They are also assumed to satisfy the functional equation \(D(p,q)=D(p,p+q)\). Furthermore, if \(D(p,-q)=D(p,q)\) for all \((p,q)\) in the domain, then \(D\) is called an even Dedekind symbol. Odd Dedekind symbols are defined similarly. It turns out that \(D(p,q)\) can be uniquely determined up to additive constants by assuming a reciprocity law (similar to the reciprocity law for the classical Dedekind sums). There are two types of reciprocity laws that are postulated in this paper. Precisely, these are called plus or minus type laws. Many consequences of the less studied plus type reciprocity laws are given. These consequences indicate fundamental differences in the behavior of Dedekind symbols satisfying plus or minus type reciprocity laws.
reviewed by: Emre Alkan
Mathematics Subject Classification ID: 11F20
Mathematics Subject Classification ID: 11A15
zbMATH DE Number: 5378825
zbMATH Keywords: Dedekind sum
zbMATH Keywords: Dedekind symbol
zbMATH Keywords: reciprocity law
MaRDI profile type: Publication
full work available at URL: j.jnt.2007.05.007
OpenAlex ID: W2014197607
cites work: Q4310750
cites work: Modular forms, generalized Dedekind symbols and period polynomials
cites work: Generalized Dedekind symbols associated with the Eisenstein series
cites work: Dedekind symbols with polynomial reciprocity laws
cites work: Q5663963
DOI: 10.1016/J.JNT.2007.05.007
description: scientific article; zbMATH DE number 5378825