Stephen Bartell, Abby Halverson, Brenden Schlader, Siena Truex, Tian An Wong
{"title":"The density of the graph of elliptic Dedekind sums","authors":"Stephen Bartell, Abby Halverson, Brenden Schlader, Siena Truex, Tian An Wong","doi":"10.1007/s11139-024-00880-z","DOIUrl":null,"url":null,"abstract":"<p>We show that the graph of normalized elliptic Dedekind sums is dense in its image for arbitrary imaginary quadratic fields, generalizing a result of Ito in the Euclidean case. We also derive some basic properties of Martin’s continued fraction algorithm for arbitrary imaginary quadratic fields.</p>","PeriodicalId":501430,"journal":{"name":"The Ramanujan Journal","volume":"21 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Ramanujan Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11139-024-00880-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We show that the graph of normalized elliptic Dedekind sums is dense in its image for arbitrary imaginary quadratic fields, generalizing a result of Ito in the Euclidean case. We also derive some basic properties of Martin’s continued fraction algorithm for arbitrary imaginary quadratic fields.