A hybrid of two theorems of Piatetski-Shapiro

Angel Kumchev, Zhivko Petrov

Let $c>1$ and $0<\gamma <1$ be real, with $c\notin \mathbb{N}$. We study the solubility of the Diophantine inequality \[ \left| p_1^c + p_2^c + \dots + p_s^c - N \right| < \varepsil…