Slim exceptional sets of Waring-Goldbach problems involving squares and cubes of primes. (English. Russian original) Zbl 1537.11128
Sb. Math. 214, No. 5, 744-756 (2023); translation from Mat. Sb. 214, No. 5, 140-152 (2023).
Authors’ abstract: Let \(p_1,p_2,\dots,p_6\) be prime numbers. First we show that, with at most \(O(N^{1/12+\varepsilon})\) exceptions, all even positive integers not exceeding \(N\) can be represented in the form \(p_1^2+p_2^2+p_3^3+p_4^3+p_5^3+p_6^3\), which improves the previous result \(O(N^{1/4+\varepsilon})\) obtained by J. Liu [Proc. Steklov Inst. Math. 276, 176–192 (2012; Zbl 1297.11130)]. Moreover, we also prove that, with at most \(O(N^{5/12+\varepsilon})\) exceptions, all even positive integers not exceeding \(N\) can be represented in the form \(p_1^2+p_2^3+p_3^3+p_4^3+p_5^3+p_6^3\).
Reviewer: Giovanni Coppola (Napoli)
MSC:
| 11P32 | Goldbach-type theorems; other additive questions involving primes |
| 11P05 | Waring’s problem and variants |
| 11P55 | Applications of the Hardy-Littlewood method |
Citations:
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| [22] | Xue Han School of Mathematics and Statistics, Shandong Normal University, Jinan, P.R. China E-mail: han_xue@stu.sdnu.edu.cn |
| [23] | Huafeng Liu School of Mathematics and Statistics, Shandong Normal University, Jinan, P.R. China E-mail: hfliu_sdu@hotmail.com |
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