{"title":"On Doi-Naganuma lifting","authors":"Balesh Kumar, M. Manickam","doi":"10.21099/TKBJM/1492104600","DOIUrl":null,"url":null,"abstract":". In this paper, we extend the Doi-Naganuma lifting as suggested by Kudla [4], on the lines of Zagier’s work [6]. For each fundamental discriminant D associated with a real quadratic field, we prove that there exists a Hecke-equivarient map i D which maps the m th Poincare series of weight k , level M and character w D ¼ : D (cid:1) (cid:2) into a Hilbert cusp form of weight k , level M = D associated with the real quadratic field of discriminant D of class number one. Through this, we get its adjoint i (cid:1) D with respect to the Petersson inner product.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.21099/TKBJM/1492104600","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tsukuba Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21099/TKBJM/1492104600","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
. In this paper, we extend the Doi-Naganuma lifting as suggested by Kudla [4], on the lines of Zagier’s work [6]. For each fundamental discriminant D associated with a real quadratic field, we prove that there exists a Hecke-equivarient map i D which maps the m th Poincare series of weight k , level M and character w D ¼ : D (cid:1) (cid:2) into a Hilbert cusp form of weight k , level M = D associated with the real quadratic field of discriminant D of class number one. Through this, we get its adjoint i (cid:1) D with respect to the Petersson inner product.