Sums Of Three Or More Primes In Arithmetic Progressions

In 1997,Friedlander and Goldston gave representable asymptotic formula of sums of three or more primes. In this thesis we extend Priedlander and Goldston's result into arithmetic progressions and give its representable asymptotic formula respectively based on the large or small moduli. The thesis consists of three chapters. In chapter 1, firstly, we introduce the research advance of Goldbach conjecture and that in arithmetic progres-sions,secondly,we give the problem which we shall study and the result which we get. In chapter 2, under small moduli,using Siegel-Walfisz theorem we get an representable asymptotic formula of sums of three or more primes in arithmetic progressions. In chapter 3, under large moduli, using the explicit formula of î—ƒ A(n)x(rc) we get the representableformula of Sj(a) and Ik(N), further, we extend the result of chapter 2.