Evaluation of the Assistant Function with Four Zeros and all Nonprincipal Characters but X1X2X3X4

Chinese Quarterly Journal of Mathematics ›› 2006, Vol. 21 ›› Issue (2): 196-201.

Evaluation of the Assistant Function with Four Zeros and all Nonprincipal Characters but X₁X₂X₃X₄

Department of Applied Mathematics,Tongji University, Shanghai 200092, China; College of Mathematics and Information Science, Henan University, Kaifeng 475001, China

Received:2005-12-20 Online:2006-06-30 Published:2023-12-05
About author:LI Yi-jun(1972-),male,native of Yanshi,Henan,engages in analytic number theory.
Supported by:
Supported by the National Natural Science Foundation of China(10171076)； Supported by the Scientific and Technical Committee Foundation of Shanghai(03JC14027)；

Abstract

Abstract: 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.

Key words: Dirichlet's character, L-function, four zeros, Goldbach's problem, Vinogradov's bound

CLC Number:

O156.4

LI Yi-jun. Evaluation of the Assistant Function with Four Zeros and all Nonprincipal Characters but X₁X₂X₃X₄[J]. Chinese Quarterly Journal of Mathematics, 2006, 21(2): 196-201.

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Evaluation of the Assistant Function with Four Zeros and all Nonprincipal Characters but X₁X₂X₃X₄

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