Taiwanese Journal of Mathematics

Exceptional Set for Sums of Unlike Powers of Primes

Min Zhang and Jinjiang Li

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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.

Article information

Taiwanese J. Math., Volume 22, Number 4 (2018), 779-811.

Received: 22 August 2017
Accepted: 26 September 2017
First available in Project Euclid: 14 October 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11P05: Waring's problem and variants 11P32: Goldbach-type theorems; other additive questions involving primes 11P55: Applications of the Hardy-Littlewood method [See also 11D85]

Waring-Goldbach problem circle method exceptional set


Zhang, Min; Li, Jinjiang. Exceptional Set for Sums of Unlike Powers of Primes. Taiwanese J. Math. 22 (2018), no. 4, 779--811. doi:10.11650/tjm/170906. https://projecteuclid.org/euclid.twjm/1507946425

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