中文摘要：

为了更好地估计Vinogradov界，需要改进关于Dirichlet特征的L-函数零点的界限．为此，前人曾经做过二个和三个零点辅助函数的估值．该文将其推广到四个零点的情形，并在全部非主特征条件下给出了辅助函数g（x1，x2，x3，x4）的估值，其估值常数为8．455711841994．

英文摘要：

To obtain a better Vinogradov＇s bound, an improved bound of zeros of L-functions of all Dirichlet＇s characters is needed. To do this, assistant function with two or three zeros have been evaluated. The assistant function g（x1, x2, x3, x4） with four zeros and all nonprineipal characters is constructed and evaluated here. And the evaluative constant obtained is 8. 455 711 841 994.