Short sums with a noninteger power of a natural number (Q2342028)

In this paper, the author obtained some asymptotic results about the trigonometric sum with a noninteger power of a natural number of the form \[ S_c(\alpha; x, y)= \sum\limits_{x-y<n\leq x} e(\alpha [n^c]), \] where \(y\geq \sqrt{2cx}\mathcal{L}^A\), \(\mathcal{L}=\ln x\), \(A\geq 1\).