On Waring-Goldbach Problem for Squares, Cubes and Higher Powers

2020/03/28 by Min Zhang, Jinjiang Li, Zhang, Min +1
Mathematics · #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.2003.12731

openalex publication_date 2020/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let P_r denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper, we generalize the result of Vaughan for ternary admissible exponent. Moreover, we use the refined admissible exponent to prove that, for 3\leqslant k\leqslant 14 and for every sufficiently large even integer n, the following equation n=x²+p₁²+p₂³+p₃³+p₄³+p₅^k is solvable with x being an almost-prime P_r(k) and the other variables primes, where r(k) is defined in Theorem. This result constitutes a deepening upon that of previous results.

Citations

• Waring–Goldbach problem: Two squares and some higher powers
• A new explicit formula in the additive theory of primes with applications II. The exceptional set in Goldbach's problem

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