Taiwanese Journal of Mathematics

Exceptional Set of Waring-Goldbach Problem with Unequal Powers of Primes

Xiaodong Zhao

Advance publication

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In this paper, it is proved that with at most $O(N^{17/42+\varepsilon})$ exceptions, all even positive integer $n$, $n \in [N/2,N]$, 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. This improves a recent result $O(N^{13/16+\varepsilon})$ due to Zhang and Li [13].

Article information

Taiwanese J. Math., Advance publication (2019), 8 pages.

First available in Project Euclid: 16 October 2019

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Digital Object Identifier

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

Waring-Goldbach problem circle method exceptional set


Zhao, Xiaodong. Exceptional Set of Waring-Goldbach Problem with Unequal Powers of Primes. Taiwanese J. Math., advance publication, 16 October 2019. doi:10.11650/tjm/191001. https://projecteuclid.org/euclid.twjm/1571191582

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