{"title":"Analytic continuation of the multiple Fibonacci zeta functions","authors":"S. S. Rout, N. K. Meher","doi":"10.3792/PJAA.94.64","DOIUrl":null,"url":null,"abstract":": In this article, we prove the meromorphic continuation of the multiple Fibonacci zeta functions of depth 2: where F n is the n -th Fibonacci number, Re ð s 1 Þ > 0 and Re ð s 2 Þ > 0 . We compute a complete list of its poles and their residues. We also prove that multiple Fibonacci zeta values at negative integer arguments are rational.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3792/PJAA.94.64","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
Abstract
: In this article, we prove the meromorphic continuation of the multiple Fibonacci zeta functions of depth 2: where F n is the n -th Fibonacci number, Re ð s 1 Þ > 0 and Re ð s 2 Þ > 0 . We compute a complete list of its poles and their residues. We also prove that multiple Fibonacci zeta values at negative integer arguments are rational.
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