Frontiers of Mathematics in China

, Volume 14, Issue 5, pp 1017–1035 | Cite as

Slim exceptional set for sums of two squares, two cubes, and two biquadrates of primes

  • Rui ZhangEmail author
Research Article


We prove that, with at most \(O(N^{\frac{17}{192}+\varepsilon})\) exceptions, all even positive integers up to N are expressible in the form p 1 2 + p 2 2 + p 3 3 + p 4 3 + p 5 4 + p 6 4 , where p1, p2, …, p6 are prime numbers. This gives large improvement of a recent result \(O(N^{\frac{13}{16}+\varepsilon})\) due to M. Zhang and J. J. Li.


Waring-Goldbach problem circle method exceptional set 


11P05 11P32 11P55 


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The author would like to express the most sincere gratitude to Prof. Zhixin Liu for his valuable advice and constant encouragement. This work was supported by the National Natural Science Foundation of China (Grant No. 11871367).


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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of MathematicsTianjin UniversityTianjinChina

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