{"title":"关于Arakawa-Kaneko zeta函数的类比及若干多个zeta值的关系","authors":"Ryo Umezawa","doi":"10.21099/TKBJM/1554170425","DOIUrl":null,"url":null,"abstract":"T. Ito defined an analog of the Arakawa-Kaneko zeta function to obtain relations among Mordell-Tornheim multiple zeta values. In this paper, we develop two things related to an analog of the Arakawa-Kaneko zeta function. One is to find an analog of the Arakawa-Kaneko zeta function of Miyagawa-type (defined by T. Miyagawa) and to obtain a relation among Miyagawa-type MZVs. The other is to find a class of zeta functions to which Ito's zeta functions of the case of general index are related.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2018-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On an analog of the Arakawa-Kaneko zeta function and relations of some multiple zeta values\",\"authors\":\"Ryo Umezawa\",\"doi\":\"10.21099/TKBJM/1554170425\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"T. Ito defined an analog of the Arakawa-Kaneko zeta function to obtain relations among Mordell-Tornheim multiple zeta values. In this paper, we develop two things related to an analog of the Arakawa-Kaneko zeta function. One is to find an analog of the Arakawa-Kaneko zeta function of Miyagawa-type (defined by T. Miyagawa) and to obtain a relation among Miyagawa-type MZVs. The other is to find a class of zeta functions to which Ito's zeta functions of the case of general index are related.\",\"PeriodicalId\":44321,\"journal\":{\"name\":\"Tsukuba Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2018-03-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tsukuba Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.21099/TKBJM/1554170425\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tsukuba Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21099/TKBJM/1554170425","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
On an analog of the Arakawa-Kaneko zeta function and relations of some multiple zeta values
T. Ito defined an analog of the Arakawa-Kaneko zeta function to obtain relations among Mordell-Tornheim multiple zeta values. In this paper, we develop two things related to an analog of the Arakawa-Kaneko zeta function. One is to find an analog of the Arakawa-Kaneko zeta function of Miyagawa-type (defined by T. Miyagawa) and to obtain a relation among Miyagawa-type MZVs. The other is to find a class of zeta functions to which Ito's zeta functions of the case of general index are related.
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