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arXiv · 2012.07067

Supercongruences of multiple harmonic $q$-sums and generalized finite/symmetric multiple zeta values

Yoshihiro Takeyama·Koji Tasaka
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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 explicate these conjectures through studies of multiple harmonic $q$-sums. We show that the (generalized) finite/symmetric multiple zeta value 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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Yoshihiro Takeyama, Koji Tasaka. 2020-12-13. Supercongruences of multiple harmonic $q$-sums and generalized finite/symmetric multiple zeta values. https://arxiv.org/abs/2012.07067

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