The sum formula is one of the most well-known relations among multiple zeta values. This paper proves a conjecture of Kaneko predicting that an analogous formula holds for finite multiple zeta values.
We introduce an algebraic formulation of the cyclic sum formulas for multiple zeta values and for multiple zeta-star values. We also present an algebraic proof of cyclic sum formulas for multiple zeta values and for multiple zeta-star values by reducing them to Kawashima's relation.
Interpolated multiple q-zeta values are deformation of multiple q-zeta values with one parameter, t, and restore classical multiple zeta values as t = 0 and q → 1. In this paper, we discuss generating functions for sum of interpolated multiple q-zeta values with fixed weight, depth and i-height. The functions are systematically expressed in terms of the basic hypergeometric functions. Compared with the result of Ohno and Zagier, our result includes three generalizations: general height, q-deformation and t-interpolation. As an application, we prove some expected relations for interpolated multiple q-zeta values including sum formulas.
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