多重调和 /i>-和与广义有限/对称多重ZETA值的超同余

IF 0.6 4区数学 Q3 MATHEMATICS

Kyushu Journal of Mathematics Pub Date : 2023-01-01 DOI:10.2206/kyushujm.77.75

Yoshihiro TAKEYAMA, Koji TASAKA

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引用次数: 4

摘要

Kaneko-Zagier猜想描述了有限多重zeta值和对称多重zeta值之间的对应关系。Jarossay, Rosen和Ono-Seki-Yamamoto建立了它的改进版本。在本文中，我们通过对多重谐波q和的研究进一步解释了这些猜想。我们证明了(广义)有限/对称多重zeta值是通过取多重调和q和的代数/解析极限得到的。作为应用，给出了广义有限/对称多重zeta值的反转、对偶和循环和公式的新证明。

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SUPERCONGRUENCES OF MULTIPLE HARMONIC q-SUMS AND GENERALIZED FINITE/SYMMETRIC MULTIPLE ZETA VALUES

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.

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来源期刊

Kyushu Journal of Mathematics 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

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.

多重调和<i> /i>-和与广义有限/对称多重ZETA值的超同余

摘要