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

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_2^3+p_3^3+p_4^3+p_5^3, 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

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Higher Education Press 2023