{"title":"SUPERCONGRUENCES OF MULTIPLE HARMONIC <i>q</i>-SUMS AND GENERALIZED FINITE/SYMMETRIC MULTIPLE ZETA VALUES","authors":"Yoshihiro TAKEYAMA, Koji TASAKA","doi":"10.2206/kyushujm.77.75","DOIUrl":null,"url":null,"abstract":"The Kaneko-Zagier conjecture describes a correspondence between finite multiple zeta values and symmetric multiple zeta values. Its refined version has been established by Jarossay, Rosen and Ono-Seki-Yamamoto. In this paper, we further explain these conjectures through studies of multiple harmonic q-sums. We show that the (generalized) finite/symmetric multiple zeta values are obtained by taking an algebraic/analytic limit of multiple harmonic q-sums. As applications, new proofs of reversal, duality and cyclic sum formulas for the generalized finite/symmetric multiple zeta values are given.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kyushu Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2206/kyushujm.77.75","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 4
Abstract
The Kaneko-Zagier conjecture describes a correspondence between finite multiple zeta values and symmetric multiple zeta values. Its refined version has been established by Jarossay, Rosen and Ono-Seki-Yamamoto. In this paper, we further explain these conjectures through studies of multiple harmonic q-sums. We show that the (generalized) finite/symmetric multiple zeta values are obtained by taking an algebraic/analytic limit of multiple harmonic q-sums. As applications, new proofs of reversal, duality and cyclic sum formulas for the generalized finite/symmetric multiple zeta values are given.
期刊介绍：
The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total.
More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.
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