论文标题
在$ k_4 $的模块化曲线
On the $K_4$ group of modular curves
论文作者
论文摘要
我们使用Goncharov和de Jeu定义的重量3的pologogarithmic复合物在组$ k_4 $的模块化曲线中构建元素。该构造在该级别上是统一的，并使用新的模块化单元作为Weierstrass $ \ wp $函数的划分值的交叉比例。这些单元提供了$ k_2 $模块化曲线的$ 3 $ - 期关系的明确三角剖分，从而导致$ k_4 $中的元素。基于数值计算和W. Wang的最新结果，我们猜想这些元素与使用Eisenstein符号定义的贝林森元素成正比。
We construct elements in the group $K_4$ of modular curves using the polylogarithmic complexes of weight 3 defined by Goncharov and De Jeu. The construction is uniform in the level and uses new modular units obtained as cross-ratios of division values of the Weierstrass $\wp$ function. These units provide explicit triangulations of the $3$-term relations in $K_2$ of modular curves, which in turn give rise to elements in $K_4$. Based on numerical computations and on recent results of W. Wang, we conjecture that these elements are proportional to the Beilinson elements defined using the Eisenstein symbol.
