Quadratic residues and non-residues for infinitely many Piatetski-Shapiro primes.

In this paper, we prove a quantitative version of the statement that every nonempty finite subset of ℕ is a set of quadratic residues for infinitely many primes of the form [ n] with 1 ≤ c ≤ 243/205. Correspondingly, we can obtain a similar result for the case of quadratic non-residues under reasonable assumptions. These results generalize the previous ones obtained by Wright in certain aspects. [ABSTRACT FROM AUTHOR]