{"title":"The signs of the Stieltjes constants associated with the Dedekind zeta function","authors":"Sumaia Saad Eddin","doi":"10.3792/pjaa.94.93","DOIUrl":null,"url":null,"abstract":"The Stieltjes constants $\\gamma_n(K)$ of a number field $K$ are the coefficients of the Laurent expansion of the Dedekind zeta function $\\zeta_K(s)$ at its pole $s=1$. In this paper, we establish a similar expression of $\\gamma_n(K)$ as Stieltjes obtained in 1885 for $\\gamma_n(\\mathbb Q)$. We also study the signs of $\\gamma_n(K)$.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Japan Academy Series A-Mathematical Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3792/pjaa.94.93","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
The Stieltjes constants $\gamma_n(K)$ of a number field $K$ are the coefficients of the Laurent expansion of the Dedekind zeta function $\zeta_K(s)$ at its pole $s=1$. In this paper, we establish a similar expression of $\gamma_n(K)$ as Stieltjes obtained in 1885 for $\gamma_n(\mathbb Q)$. We also study the signs of $\gamma_n(K)$.
期刊介绍：
The aim of the Proceedings of the Japan Academy, Series A, is the rapid publication of original papers in mathematical sciences. The paper should be written in English or French (preferably in English), and at most 6 pages long when published. A paper that is a résumé or an announcement (i.e. one whose details are to be published elsewhere) can also be submitted.
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