数域和模曲线的K-群及其欧拉系统的研究

本项目计划研究数域的代数整数环的Milnor群的2^n-rank和p-rank的分布以及密度问题，椭圆曲线的Mahler测度与L-函数的值之间的关系，椭圆双对数与L-函数之间关系（Zagier猜想）， K群与高阶正规化子的关系，模曲线的欧拉系统以及其在高维正交群上的推广。

This project will study the density problem of the 2^n-rank and p-rank of the Milnor K-groups of rings of integers of algebraic number fields,the relation between the Mahler measure and L-values, elliptic dilogarithm and L-functions of elliptic curves （Zagier'sconjecture）, algebraic K-groups and regulators, the Euler system of modular curves and its generalization to orthogonal groups.