Affiliation:
1. School of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou, Henan 450046, China
Abstract
Abstract
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.,
$\begin{array}{}
N=p_1^3+ \ldots +p_j^3
\end{array} $ with
$\begin{array}{}
|p_i-(N/j)^{1/3}|\leq N^{1/3- \delta +\varepsilon} (1\leq i\leq j),
\end{array} $ for some
$\begin{array}{}
0 \lt \delta\leq\frac{1}{90}.
\end{array} $ Furthermore, we give the quantitative relations between the length of short intervals and the size of exceptional sets.
Reference50 articles.
1. On sums of powers of almost equal primes;Proc. London Math. Soc.,2015