On the distribution of $\hat{I}\pm p^2$ modulo one over primes of the form $[n^c]$

S. I. Dimitrov, M. D. Lazarova

Let $[\cdot ]$ be the floor function and $\Vert x\Vert$ denote the distance from $x$ to the nearest integer. In this paper we show that whenever $\hat{I}\pm$ is irrational and ${\hat{I}}^2$ is real th…