A Density Theorem for Higher Order Sums of Prime Numbers

2024/11/02 by Michael T. Lacey, Lacey, Michael T., Hamed Mousavi +5
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2411.01296

openalex publication_date 2024/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let P be a subset of the primes of lower density strictly larger than \frac12. Then, every sufficiently large even integer is a sum of four primes from the set P. We establish similar results for k-summands, with k≥ 4, and for k ≥ 4 distinct subsets of primes. This extends the work of H.~Li, H.~Pan, as well as X.~Shao on sums of three primes, and A.~Alsteri and X.~Shao on sums of two primes. The primary new contributions come from elementary combinatorial lemmas.

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