Quantitative relations between short intervals and exceptional sets of cubic Waring-Goldbach problem

Zhao Feng

Zhao Feng

Open Mathematics, Tome 15 (2017), p. 1517-1529 / Harvested from The Polish Digital Mathematics Library

Résumé

In this paper, we are able to prove that almost all integers n satisfying some necessary congruence conditions are the sum of j almost equal prime cubes with j = 7, 8, i.e., [...] N=p13+…+pj3 $\begin{matrix} N = p_{1}^{3} + ... + p_{j}^{3} \end{matrix}$ with [...] |pi−(N/j)1/3|≤N1/3−δ+ε(1≤i≤j), $\begin{matrix} | p_{i} - {(N / j)}^{1 / 3} | \leq N^{1 / 3 - δ + ε} (1 \leq i \leq j), \end{matrix}$ for some [...] 0<δ≤190. $\begin{matrix} 0 δ \leq \frac{1}{90} . \end{matrix}$ Furthermore, we give the quantitative relations between the length of short intervals and the size of exceptional sets.

Publié le : 2017-01-01
EUDML-ID : urn:eudml:doc:288293

@article{bwmeta1.element.doi-10_1515_math-2017-0130,
     author = {Zhao Feng},
     title = {Quantitative relations between short intervals and exceptional sets of cubic Waring-Goldbach problem},
     journal = {Open Mathematics},
     volume = {15},
     year = {2017},
     pages = {1517-1529},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0130}
}

Zhao Feng. Quantitative relations between short intervals and exceptional sets of cubic Waring-Goldbach problem. Open Mathematics, Tome 15 (2017) pp. 1517-1529. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0130/