On the number of representations of integers as differences between Piatetski-Shapiro numbers

Yuuya Yoshida

For $\alpha >1$, set $\beta =1/(\alpha -1)$. We show that, for every $1<\alpha <(\sqrt{21}+4)/5\approx 1.717$, the number of pairs $(m,n)$ of positive integers with $d=\lfloor{n^α}\rfloor - \lfloor{m^α}\r…