The additive problem with one cube and three cubes of primes. (English) Zbl 1360.11092
Summary: In this paper, we establish that all positive integers up to \(N\) but at most \(O(N^{25/27+\varepsilon})\) exceptions can be represented as the sum of a cube and three cubes of primes. This improves upon the earlier result \(O(N^{17/18+\varepsilon})\) obtained by X. Ren and K.-M. Tsang [Mich. Math. J. 53, No. 3, 571–577 (2005; Zbl 1101.11044)].
MSC:
| 11P32 | Goldbach-type theorems; other additive questions involving primes |
| 11P05 | Waring’s problem and variants |
| 11P55 | Applications of the Hardy-Littlewood method |
Citations:
Zbl 1101.11044References:
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