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- Title
An improvement on Waring-Goldbach problem for unlike powers.
- Authors
Liu, Zhixin
- Abstract
Let p be prime numbers. In this paper, it is proved that for any integer k≧5, with at most $O\big(N^{1-\frac{1}{3k\times2^{k-2}}+\varepsilon}\big)$ exceptions, all positive even integers up to N can be expressed in the form $p_{2}^{2}+p_{3}^{3}+p_{5}^{5}+p_{k}^{k}$. This improves the result $O\big(\frac{N}{\log^{c}N}\big)$ for some c>0 due to Lu and Shan [12], and it is a generalization for a series of results of Ren and Tsang [15], [16] and Bauer [1-4] for the problem in the form $p_{2}^{2}+p_{3}^{3}+p_{4}^{4}+p_{5}^{5}$. This method can also be used for some other similar forms.
- Subjects
GOLDBACH conjecture; WARING'S problem; MATHEMATICAL analysis; MATHEMATICAL proofs; PRIME numbers; SET theory; CIRCLE
- Publication
Acta Mathematica Hungarica, 2011, Vol 130, Issue 1/2, p118
- ISSN
0236-5294
- Publication type
Article
- DOI
10.1007/s10474-010-0002-1