Exceptional sets for sums of almost equal prime cubes. (English) Zbl 1470.11248
Summary: In this paper, we continue to investigate the exceptional sets for sums of five and six almost equal cubes of primes. We would also like to establish that almost all natural numbers \(n\), subjected to certain congruence conditions, can be written as \(n=p_1^3+\cdots+p_s^3 (s=5,6)\) with \(|p_j-(n/s)^{1/3}|\leq n^{\theta_s/3+\varepsilon} (1\leq j\leq s)\), where \(\theta_s\) is as small as possible. The main result of this paper is to improve \(\theta_6=5/6+\varepsilon \), which is proven in [the author, Acta Math. Hung. 156, No. 2, 424–434 (2018; Zbl 1424.11146)], to \(\theta_6=9/11+\varepsilon \), as well as prove \(\theta_5=8/9+\varepsilon\) in another way.
Citations:
Zbl 1424.11146References:
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