Small gaps between the Piatetski-Shapiro primes

Abstract

Suppose that $1<c<9/8$. For any $m\ge 1$, there exist infinitely many $n$ such that $$\{[n^c],[(n+1{)}^c],\dots ,[(n+k_0{)}^c]\}$$ contains at least $m+1$ primes, if $k_0$ is sufficiently large (only depending on $m$).

This is a very preliminary draft, which maybe contains some mistakes

References in corpus (1)

• Bounded gaps between primes with a given primitive root