The ternary Goldbach problem with the Piatetski-Shapiro primes

Abstract

With the help of the transference principle, we prove that for any $c_1,c_2,c_3\in(1,73/64)$, every sufficiently large odd $n$ can be represented as the sum of three primes $p_1$, $p_2$ and $p_3$, where for each $1\leq i\leq 3$, $p_i$ is of the form $\lfloor n^{c_i}\rfloor$.Comment: This is a very preliminary manuscript, which maybe contains some mistake