论冈察洛夫深度猜想和深度为 2 的多项式

Selecta Mathematica Pub Date : 2024-02-22 DOI:10.1007/s00029-024-00918-6

Steven Charlton, Herbert Gangl, Danylo Radchenko, Daniil Rudenko

引用次数: 0

摘要

我们证明了冈察洛夫在二次封闭域上的深度猜想的可射性部分。我们还证明了深度猜想意味着深度为 d、权重为 n 的多个多项式可以通过一个函数 ${{\,\textrm{Li}\,}}_{n-d+1,1,\dots ,1}(a_1,a_2,\dots ,a_d)$ 来表达，并且我们证明了后$d=2$的这一声明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the Goncharov depth conjecture and polylogarithms of depth two

We prove the surjectivity part of Goncharov’s depth conjecture over a quadratically closed field. We also show that the depth conjecture implies that multiple polylogarithms of depth d and weight n can be expressed via a single function ${{\,\textrm{Li}\,}}_{n-d+1,1,\dots ,1}(a_1,a_2,\dots ,a_d)$, and we prove this latter statement for $d=2$.

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