Geodesic
Slim exceptional sets of Waring--Goldbach problem: two squares, two cubes and two biquadrates
Sbornik. Mathematics, Tome 216 (2025) no. 1, pp. 87-98

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $N$ be a sufficiently large number. We show that, with at most $O(N^{3/32+\varepsilon})$ exceptions, all even positive integers not exceeding $N$ can be represented in the form $p_1^2+p_2^2+p_3^3+p_4^3+p_5^4+p_6^4$, where $p_1, p_2, \dots, p_6$ are prime numbers. This is an improvement of the result $O(N^{7/18+\varepsilon})$ due to Zhang and Li. Bibliography: 13 titles.
Keywords: Waring–Goldbach problem, Hardy–Littlewood method, exceptional set. 
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     title = {Slim exceptional sets of {Waring--Goldbach} problem: two squares, two cubes and two biquadrates},
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Sh. Tian. Slim exceptional sets of Waring--Goldbach problem: two squares, two cubes and two biquadrates. Sbornik. Mathematics, Tome 216 (2025) no. 1, pp. 87-98. http://geodesic.mathdoc.fr/item/SM_2025_216_1_a4/