ON THE TERNARY GOLDBACH PROBLEM WITH PRIMES IN INDEPENDENT ARITHMETIC PROGRESSIONS

摘要

We show that for every fixed A > 0 and θ > 0 there is a # = 0(A, θ) > 0 with the following property Let n be odd and sufficiently large, and let Qx = Q2 := n1/2(logn)-0 and Q3: (logn)θ. Then for all q3 ≤ Q3, all reduced residues a_3 mod q_3, almost all q_2≤Q_2, all admissible residues a_2 mod q_2, almost all q_1≤Q_1 and all admissible residues a_1 mod q_1, there exists a representation n=p_1+p_2+p_3 with primes p_i=a_i(qi),i=1,2,3.