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

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  • TAKEYAMA Yoshihiro
    Department of Mathematics Faculty of Pure and Applied Sciences University of Tsukuba
  • TASAKA Koji
    Department of Information Science and Technology Aichi Prefectural University

抄録

<p>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.</p>

収録刊行物

  • 九州数学雑誌

    九州数学雑誌 77 (1), 75-120, 2023

    九州大学大学院数理学研究院

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