On variants of symmetric multiple zeta-star values and the cyclic sum formula
On variants of symmetric multiple zeta-star values and the cyclic sum formula
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对称多重 zeta 星值的变体及循环和公式
DOI：
10.1007/s11139-020-00341-3
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Ono Masataka
中科院分区：
文献类型：
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作者：
Hirose Minoru;Murahara Hideki;Ono Masataka
Thet-adic对称多重zeta值由Jarossay定义，它被研究为$${\varvec{p}}$$-adic有限多重zeta值的真实的模拟。在本文中，我们考虑基于多zeta-星星值的几种正则化过程的星星模拟：调和正则化，洗牌正则化，Kaneko-Yamamoto的类型正则化。给出了-adic对称多重zeta（-星星）值的循环和公式，它是川崎给出的$${\varvec{p}}$$-adic有限多重zeta（-星星）值的循环和公式的对应.证明使用我们的新的关系，连接循环和公式为进对称的多个zeta-星值和，为多个zeta-星值。
Thet-adic symmetric multiple zeta values were defined by Jarossay, which have been studied as a real analogue of the $${\varvec{p}}$$-adic finite multiple zeta values. In this paper, we consider the star analogues based on several regularization processes of multiple zeta-star values: harmonic regularization, shuffle regularization, and Kaneko–Yamamoto’s type regularization. We also present the cyclic sum formula fort-adic symmetric multiple zeta(-star) values, which is the counterpart of that for $${\varvec{p}}$$-adic finite multiple zeta(-star) values obtained by Kawasaki. The proof uses our new relationship that connects the cyclic sum formula fort-adic symmetric multiple zeta-star values and that for the multiple zeta-star values.