Cubic Waring-Goldbach problem with Piatetski-Shapiro primes

TL;DR

This paper proves that sufficiently large odd integers can be expressed as sums of nine cubes of Piatetski-Shapiro primes within a specific range of b gamma, improving previous results in the field.

Contribution

It establishes a new result for the Waring-Goldbach problem involving Piatetski-Shapiro primes for b gamma in (17/320,1), advancing the understanding of prime representations.

Findings

Every large odd integer is sum of nine cubes of Piatetski-Shapiro primes for b b gamma in (17/320,1)

Improves previous bounds on the representation of integers as sums of prime cubes

Extends the classical Waring-Goldbach problem to a new class of primes.

Abstract

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