On the ternary Goldbach problem with primes in independent arithmetic progressions

Karin Halupczok

paper

On the ternary Goldbach problem with primes in independent arithmetic progressions

arXiv:0803.0831

Abstract

We show that for every fixed $A > 0$ and $θ > 0$ there is a $ϑ = ϑ (A, θ) > 0$ with the following property. Let $n$ be odd and sufficiently large, and let $Q_{1}=Q_{2}:=n^{\h}(\log n)^{-\vartheta}$ and $Q_{3} := (lo g n)^{θ}$ . Then for all $q_{3} \leq Q_{3}$ , all reduced residues $a_{3}$ mod $q_{3}$ , almost all $q_{2} \leq Q_{2}$ , all admissible residues $a_{2}$ mod $q_{2}$ , almost all $q_{1} \leq Q_{1}$ and all admissible residues $a_{1}$ mod $q_{1}$ , there exists a representation $n = p_{1} + p_{2} + p_{3}$ with primes $p_{i} \equiv a_{i} (q_{i})$ , $i = 1, 2, 3$ .

accepted for publication in Acta Math. Hungar