TY - JOUR
T1 - Yamamoto’s Interpolation of Finite Multiple Zeta and Zeta-star Values
AU - Murahara, Hideki
AU - Ono, Masataka
N1 - Funding Information:
Received August 26, 2019; revised August 24, 2020 2010 Mathematics Subject Classification: 11M32 (Primary), 05A19 (Secondary) Key words and phrases: Multiple zeta(-star) values, Interpolated multiple zeta values, values, Symmetric multiple zeta(-star) values This research was supported in part by JSPS KAKENHI Grant Number JP16H06336.
Publisher Copyright:
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PY - 2021/12
Y1 - 2021/12
N2 - 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.
AB - 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.
KW - Finite multiple zeta(-star) values
KW - Interpolated multiple zeta values
KW - Multiple zeta(-star) values
KW - Symmetric multiple zeta(-star) values
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U2 - 10.3836/tjm/1502179339
DO - 10.3836/tjm/1502179339
M3 - Article
AN - SCOPUS:85118708220
SN - 0387-3870
VL - 44
SP - 285
EP - 312
JO - Tokyo Journal of Mathematics
JF - Tokyo Journal of Mathematics
IS - 2
ER -