Yamamoto's interpolation of finite multiple zeta and zeta-star values

Abstract

We study a polynomial interpolation of finite multiple zeta and zeta-star values with variable $t$, which is an analogue of interpolated multiple zeta values introduced by Yamamoto. We introduce several relations among them and, in particular, prove the cyclic sum formula, the Bowman-Bradley type formula, and the weighted sum formula. The harmonic relation, the shuffle relation, the duality relation, and the derivation relation are also presented.

24 pages, 2 figures

References in corpus (6)

• Cyclotomic analogues of finite multiple zeta values
• On variants of symmetric multiple zeta-star values and the cyclic sum formula
• A note on derivation relations for multiple zeta values and finite multiple zeta values
• Algebraic relations of interpolated multiple zeta values
• A cyclic analogue of multiple zeta values
• Use of the generating function to generalize the sum formula for quadruple zeta values

Cited by in corpus (2)

• On variants of symmetric multiple zeta-star values and the cyclic sum formula
• Recurrent Sums and Partition Identities