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On multiple polylogarithms in characteristic $p$: $v$-adic vanishing versus $\infty$-adic Eulerian

Chieh-Yu Chang National Tsing Hua University Yoshinori Mishiba National Institute of Technology, Oyama College

Number Theory mathscidoc:1610.24008

In this paper, we give a simultaneous vanishing principle for the $v$-adic Carlitz multiple polylogarithms (abbreviated as CMPLs) at algebraic points, where $v$ is a finite place of the rational function field over a finite field. This principle establishes the fact that the $v$-adic vanishing of CMPLs at algebraic points is equivalent to its $\infty$-adic counterpart being Eulerian. This reveals a nontrivial connection between the $v$-adic and $\infty$-adic worlds in positive characteristic.
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@inproceedings{chieh-yuon,
  title={On multiple polylogarithms in characteristic $p$: $v$-adic vanishing versus $\infty$-adic Eulerian},
  author={Chieh-Yu Chang, and Yoshinori Mishiba},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161021172041904765596},
}
Chieh-Yu Chang, and Yoshinori Mishiba. On multiple polylogarithms in characteristic $p$: $v$-adic vanishing versus $\infty$-adic Eulerian. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161021172041904765596.
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