Establish Kaneko–Zagier-type relations for p-adic finite multiple zeta values

Establish that p-adic finite multiple zeta values satisfy relations of the same form as those satisfied by t-adic symmetric multiple zeta values, as suggested by the generalized Kaneko–Zagier conjecture, thereby proving these relations for the p-adic finite setting.

Background

The paper proves a conjectured polynomial expression modulo t^2 for t-adic symmetric multiple zeta values associated with indices ({1,3}^n), extending prior work on such structures and showing that these values can be expressed in terms of Riemann zeta values.

Motivated by the generalized Kaneko–Zagier conjecture, the authors note that analogous relations are expected to hold for p-adic finite multiple zeta values. However, while the t-adic symmetric multiple zeta values satisfy certain relations, it remains unproven that p-adic finite multiple zeta values obey relations of the same form.