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

doi:10.1007/s11464-019-0794-4

Front. Math. China

2019, Vol. 14

Issue (5) : 1017-1035 https://doi.org/10.1007/s11464-019-0794-4

RESEARCH ARTICLE

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

Rui ZHANG(

)

School of Mathematics, Tianjin University, Tianjin 300350, China

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Abstract

We prove that, with at most $O (N 17192 + ε)$ exceptions, all even positive integers up to Nare expressible in the form $p 12 + p 22 + p 33 + p 43 + p 54 + p 64$ ,where $p 1, p 2, . . ., p 6$ are prime numbers. This gives large improvement of a recent result $O (N 1316 + ε)$ due to M. Zhang and J. J. Li.

Keywords Waring-Goldbach problem circle method exceptional set

Corresponding Author(s): Rui ZHANG

Issue Date: 22 November 2019

Cite this article:

Rui ZHANG. Slim exceptional set for sums of two squares, two cubes, and two biquadrates of primes[J]. Front. Math. China, 2019, 14(5): 1017-1035.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-019-0794-4
https://academic.hep.com.cn/fmc/EN/Y2019/V14/I5/1017

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