{"title":"与算术函数相关的二重狄利克雷级数II","authors":"Kohji Matsumoto, Hirofumi Tsumura","doi":"10.2996/kmj46102","DOIUrl":null,"url":null,"abstract":"This paper is a continuation of our previous work on double Dirichlet series associated with arithmetic functions such as the von Mangoldt function, the M\\\"obius function, and so on. We consider the analytic behaviour around the non-positive integer points on singularity sets which are points of indeterminacy. In particular, we show a certain reciprocity law of their residues. Also on this occasion we correct some inaccuracies in our previous paper.","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2022-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Double Dirichlet series associated with arithmetic functions II\",\"authors\":\"Kohji Matsumoto, Hirofumi Tsumura\",\"doi\":\"10.2996/kmj46102\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper is a continuation of our previous work on double Dirichlet series associated with arithmetic functions such as the von Mangoldt function, the M\\\\\\\"obius function, and so on. We consider the analytic behaviour around the non-positive integer points on singularity sets which are points of indeterminacy. In particular, we show a certain reciprocity law of their residues. Also on this occasion we correct some inaccuracies in our previous paper.\",\"PeriodicalId\":54747,\"journal\":{\"name\":\"Kodai Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-08-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Kodai Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2996/kmj46102\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kodai Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2996/kmj46102","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Double Dirichlet series associated with arithmetic functions II
This paper is a continuation of our previous work on double Dirichlet series associated with arithmetic functions such as the von Mangoldt function, the M\"obius function, and so on. We consider the analytic behaviour around the non-positive integer points on singularity sets which are points of indeterminacy. In particular, we show a certain reciprocity law of their residues. Also on this occasion we correct some inaccuracies in our previous paper.
期刊介绍:
Kodai Mathematical Journal is edited by the Department of Mathematics, Tokyo Institute of Technology. The journal was issued from 1949 until 1977 as Kodai Mathematical Seminar Reports, and was renewed in 1978 under the present name. The journal is published three times yearly and includes original papers in mathematics.