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

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.

51 pages

References in corpus (3)

• A $q$-microscope for supercongruences
• On variants of symmetric multiple zeta-star values and the cyclic sum formula
• Truncated $t$-adic symmetric multiple zeta values and double shuffle relations

Cited by in corpus (1)

• A note on ${\mathcal{F}}_n$-multiple zeta values