Taiwanese Journal of Mathematics

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

Xiaodong Zhao

Advance publication

This article is in its final form and can be cited using the date of online publication and the DOI.

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 16 October 2019

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1571191582

Digital Object Identifier
doi:10.11650/tjm/191001

Subjects
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]

Keywords
Waring-Goldbach problem circle method exceptional set

Citation

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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