Truncated t-adic symmetric multiple zeta values and double shuffle relations
Truncated t-adic symmetric multiple zeta values and double shuffle relations
复制标题
截断的t-adic对称多zeta值和双洗牌关系
DOI：
10.1007/s40993-021-00241-5
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发表时间：
2021
影响因子：
0.8
通讯作者：
Shuji Yamamoto
中科院分区：
文献类型：
--
作者：
Masataka Ono;Shin-ichiro Seki;Shuji Yamamoto
我们通过考虑其有限截断来研究对称多重 zeta 值的改进，称为 thet-adic 对称多重 zeta 值。更准确地说，两种正则化（调和和洗牌）给出了两种三进对称多重 zeta 值，因此我们相应地引入了两种截断。然后我们证明我们的截断趋于相应的 t-adic 对称多重 zeta 值，并分别满足调和关系和洗牌关系。这给出了双洗牌关系 fort-adic 对称多重 zeta 值的新证明，最初由 Jarossay 证明。为了证明洗牌关系，我们发展了与 2 色有根树相关的截断-adic 对称多重 zeta 值理论。最后，我们讨论了 Kaneko-Zagier 猜想的改进和 Mordell-Tornheim 类型的 t-adic 对称多重 zeta 值。
We study a refinement of the symmetric multiple zeta value, called thet-adic symmetric multiple zeta value, by considering its finite truncation. More precisely, two kinds of regularizations (harmonic and shuffle) give two kinds of thet-adic symmetric multiple zeta values, thus we introduce two kinds of truncations correspondingly. Then we show that our truncations tend to the correspondingt-adic symmetric multiple zeta values, and satisfy the harmonic and shuffle relations, respectively. This gives a new proof of the double shuffle relations fort-adic symmetric multiple zeta values, first proved by Jarossay. In order to prove the shuffle relation, we develop the theory of truncatedt-adic symmetric multiple zeta values associated with 2-colored rooted trees. Finally, we discuss a refinement of Kaneko–Zagier’s conjecture and thet-adic symmetric multiple zeta values of Mordell–Tornheim type.