{"title":"多重 Hurwitz zeta 函数的加权和公式","authors":"Shuta Hashimoto, Takashi Nakamura, Tatsuki Watanabe","doi":"10.1007/s13226-024-00675-4","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we give weighted sum formulas of the multiple Hurwitz zeta functions <span>\\(\\zeta (s_1, \\ldots , s_n;a)\\)</span>. As a corollary, we prove a well known explicit evaluation formula for <span>\\(\\zeta (s, \\ldots , s;a)\\)</span>.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"3 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Weighted sum formulas of multiple Hurwitz zeta functions\",\"authors\":\"Shuta Hashimoto, Takashi Nakamura, Tatsuki Watanabe\",\"doi\":\"10.1007/s13226-024-00675-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we give weighted sum formulas of the multiple Hurwitz zeta functions <span>\\\\(\\\\zeta (s_1, \\\\ldots , s_n;a)\\\\)</span>. As a corollary, we prove a well known explicit evaluation formula for <span>\\\\(\\\\zeta (s, \\\\ldots , s;a)\\\\)</span>.</p>\",\"PeriodicalId\":501427,\"journal\":{\"name\":\"Indian Journal of Pure and Applied Mathematics\",\"volume\":\"3 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indian Journal of Pure and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s13226-024-00675-4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indian Journal of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s13226-024-00675-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Weighted sum formulas of multiple Hurwitz zeta functions
In this paper, we give weighted sum formulas of the multiple Hurwitz zeta functions \(\zeta (s_1, \ldots , s_n;a)\). As a corollary, we prove a well known explicit evaluation formula for \(\zeta (s, \ldots , s;a)\).
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