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

Yoshihiro TAKEYAMA; Koji TASAKA

doi:10.2206/kyushujm.77.75

著者情報

キーワード: multiple zeta value, finite multiple zeta value, symmetric multiple zeta value, the Kaneko-Zagier conjecture, p-adic multiple zeta value, q-analogue of multiple zeta value, multiple harmonic q-sum, q-supercongruences

ジャーナルフリー

2023 年 77 巻 1 号 p. 75-120

DOI https://doi.org/10.2206/kyushujm.77.75

詳細

抄録

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.

責任著者(Corresponding author)

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