Cubic Waring-Goldbach problem with Piatetski-Shapiro primes

Abstract

In this paper, it is proved that, for ${\hat{I}}^3\in (\frac{317}{320},1)$, every sufficiently large odd integer can be written as the sum of nine cubes of primes, each of which is of the form $[n^{1/{\hat{I}}^3}]$. This result constitutes an improvement upon the previous result of Akbal and Güloğlu [1].

17 pages