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

doi:10.3868/s140-DDD-023-0008-x

Front. Math. China

2023, Vol. 18

Issue (2) : 139-146 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(

)

Department of Mathematics, Nanchang University, Nanchang 330031, China

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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 $n = p 1 k + p 23 + p 33 + p 43 + p 53$ , where $p 1, p 2, p 3, p 4, p 5$ are prime numbers. This expands the previous results.

Keywords Hardy−Littlewood method Waring−Goldbach problem Riemann Hypothesis short intervals

Corresponding Author(s): Liqun HU

About author:

Peng Lei and Charity Ngina Mwangi contributed equally to this work.

Online First Date: 19 October 2023 Issue Date: 13 November 2023

Cite this article:

Xiaoming PAN,Liqun HU. Waring−Goldbach problem for one prime power and four prime cubes under Riemann Hypothesis[J]. Front. Math. China, 2023, 18(2): 139-146.

URL:

https://academic.hep.com.cn/fmc/EN/10.3868/s140-DDD-023-0008-x
https://academic.hep.com.cn/fmc/EN/Y2023/V18/I2/139

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