摘要
To obtain a better Vinogradov's bound, assistant function with two or three zeros and all Dirichlet's characters has been evaluated. Assistant function g(X1,X2,X3,X4)with four zeros and all nonprincipal characters but X1X2X3X4 is constructed and evaluated in the paper. And the constant obtained is 8.395 511 841 994.
To obtain a better Vinogradov＇s bound, assistant function with two or three zeros and all Dirichlet＇s characters has been evaluated. Assistant function g（x1, x2, x3, x4） with four zeros and all nonprincipal characters but x1x2x3x4 is constructed and evaluated in the paper. And the constant obtained is 8.395 511 841 994.
基金
Supported by the National Natural Science Foundation of China(10171076)
Supported by the Scientific and Technical Committee Foundation of Shanghai(03JC14027)
关键词
L-函数
GOLDBACH问题
辅助函数
解析理论
Dirichlet＇s character
L-function
four zeros
Goldbach＇s problem
Vinogradov＇s bound
