On Multiple Polylogarithms in Characteristic $p$: $v$-Adic Vanishing Versus $\infty$-Adic Eulerianness
On Multiple Polylogarithms in Characteristic $p$: $v$-Adic Vanishing Versus $\infty$-Adic Eulerianness
复制标题
论特征 $p$ 中的多重多对数：$v$-Adic 消失与 $infty$-Adic 欧拉性
DOI：
10.1093/imrn/rnx151
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发表时间：
2017
影响因子：
1
通讯作者：
Mishiba Yoshinori
中科院分区：
文献类型：
--
作者：
Chang Chieh-Yu;Mishiba Yoshinori
本文给出了有理函数域在有限域上的有限处的多重Carlitz多对数在代数点上的同时消元原理。这一原理证明了CMPL在代数点上的-进消失等价于它的-进对应的欧拉性。这揭示了积极特征中的非平凡联系和非平凡的世界。
In this article, we give a simultaneous vanishing principle for the-adic Carlitz multiple polylogarithms (CMPLs) at algebraic points, whereis a finite place of the rational function field over a finite field. This principle establishes the fact that the-adic vanishing of CMPLs at algebraic points is equivalent to its-adic counterpart being Eulerian. This reveals a nontrivial connection between the-adic and-adic worlds in positive characteristic.