Exceptional set for sums of unlike powers of primes. (English) Zbl 1443.11204

Zhang, Min; Li, Jinjiang

Taiwanese J. Math. 22, No. 4, 779-811 (2018).

Summary: Let \(N\) be a sufficiently large integer. In this paper, it is proved that with at most \(O(N^{13/16+\varepsilon})\) exceptions, all even positive integers up to \(N\) 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 \(p_1\), \(p_2\), \(p_3\), \(p_4\), \(p_5\), \(p_6\) are prime numbers.

MSC:

11P05	Waring’s problem and variants
11P32	Goldbach-type theorems; other additive questions involving primes
11P55	Applications of the Hardy-Littlewood method

Keywords:

Waring-Goldbach problem; circle method; exceptional set

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