The ternary Goldbach problem with primes in positive density sets

2016/02/27 by Quanli Shen, Shen, Quanli · 2 citations
Mathematics · #11B05 #11P32 #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1603.00004

openalex publication_date 2016/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let P denote the set of all primes. P₁,P₂,P₃ are three subsets of P. Let \underlineδ(P_i) (i=1,2,3) denote the lower density of P_i in P, respectively. It is proved that if \underlineδ(P₁)>5/8, \underlineδ(P₂)≥5/8, and \underlineδ(P₃)≥5/8, then for every sufficiently large odd integer n, there exist p_i ∈ P_i such that n=p₁+p₂+p₃. The condition is the best possible.

Citations

• The ternary Goldbach conjecture is true

Cited by

• Problems 66 and 67 on sums of residue classes and primes of András Sárközy's collection of unsolved problems
• Density ternary Goldbach for primes in a fixed residue class

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