Frontiers of Mathematics in China >

2023 , Vol. 18 >Issue 2: 139 - 146

DOI: https://doi.org/10.3868/s140-DDD-023-0008-x

RESEARCH　ARTICLE

Waring−Goldbach problem for one prime power and four prime cubes under Riemann Hypothesis

  • Xiaoming PAN ,
  • Liqun HU
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  • Department of Mathematics, Nanchang University, Nanchang 330031, China
huliqun@ncu.edu.cn

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2023 Higher Education Press 2023
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Abstract

Let k⩾1 be an integer. Assume that RH holds. In this paper we prove that a suitable asymptotic formula for the average number of representations of integers n=p1k+p23+p33+p43+p53, where p1,p2,p3,p4,p5 are prime numbers. This expands the previous results.

Key words： Hardy−Littlewood method; Waring−Goldbach problem; Riemann Hypothesis; short intervals

Cite this article

Xiaoming PAN , Liqun HU . Waring−Goldbach problem for one prime power and four prime cubes under Riemann Hypothesis[J]. Frontiers of Mathematics in China, 2023 , 18(2) : 139 -146 . DOI: 10.3868/s140-DDD-023-0008-x

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 11761048), the Natural Science Foundation of Jiangxi Province for Distinguished Young Scholars (Grant No. 20212ACB211007) and Natural Science Foundation of Jiangxi Province (Grant No. 20224BAB201001).

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