Bloch Group, K Group And Zeta Function Of Special Value

In this paper, we mainly study a commutative diagram of regulators between the Bloch group and the K3 group. Firstly, we introuduce the background of the problem. Then,in chapterⅠwe state some definitions and propositions for the proof, including the definitions of the Bloch group and K3 group as well as their properties. In chapterⅡ, we construct the three maps in the diagram and then we show that they are commutative. In chapterⅢ, we present disscusions on two relative problems. In the first one, we disproves a conjecture of Browkin on relation between the special value of Zeta function and regulator, and in the second one we verify the famouse Lichtenbaum’s conjectue for a special quadratic complex field.