Geodesic
Slim exceptional sets of Waring-Goldbach problems involving squares and cubes of primes
Sbornik. Mathematics, Tome 214 (2023) no. 5, pp. 744-756 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 Y. H. Liu. 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 $p_{1}^{2}+p_{2}^{3}+p_{3}^{3}+p_{4}^{3}+p_{5}^{3}+p_{6}^{3}$. Bibliography: 21 titles.
Keywords: Waring-Goldbach problem, exceptional set, Hardy-Littlewood method. 
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X. Han; H. Liu. Slim exceptional sets of Waring-Goldbach problems involving squares and cubes of primes. Sbornik. Mathematics, Tome 214 (2023) no. 5, pp. 744-756. http://geodesic.mathdoc.fr/item/SM_2023_214_5_a5/

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