论文标题
截短的$ t $ - adic对称的多个Zeta值和双层式关系
Truncated $t$-adic symmetric multiple zeta values and double shuffle relations
论文作者
论文摘要
我们通过考虑其有限的截断来研究对称的多重Zeta值的改进，称为$ t $ ADIC对称的多重Zeta值。更确切地说，两种正规化（谐波和散装）给出了两种$ t $ - ad-adic对称的多重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向于相应的$ t $ - 亚种对称多重Zeta值，并分别满足谐波和洗牌关系。这为$ t $ addic对称的多个Zeta值提供了新的证明，这是Jarossay首先证明的。为了证明洗牌关系，我们发展了截断的$ t $ t $对称对称的多重Zeta值与$ 2 $颜色的扎根树相关的理论。最后，我们讨论了Kaneko-Zagier的猜想和Mordell-Tornheim类型的$ T $ ADIC对称的多重Zeta值的改进。
We study a refinement of the symmetric multiple zeta value, called the $t$-adic symmetric multiple zeta value, by considering its finite truncation. More precisely, two kinds of regularizations (harmonic and shuffle) give two kinds of the $t$-adic symmetric multiple zeta values, thus we introduce two kinds of truncations correspondingly. Then we show that our truncations tend to the corresponding $t$-adic symmetric multiple zeta values, and satisfy the harmonic and shuffle relations, respectively. This gives a new proof of the double shuffle relations for $t$-adic symmetric multiple zeta values, first proved by Jarossay. In order to prove the shuffle relation, we develop the theory of truncated $t$-adic symmetric multiple zeta values associated with $2$-colored rooted trees. Finally, we discuss a refinement of Kaneko-Zagier's conjecture and the $t$-adic symmetric multiple zeta values of Mordell-Tornheim type.
