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

Abstract

In this paper, we prove a quantitative version of the statement that every nonempty finite subset of ${\mathbb{N}}^{+}$ is a set of quadratic residues for infinitely many primes of the form $[n^c]$ 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 S. Wright in certain aspects.

arXiv comment9 pages, to appear in Acta Math. Sinica, English Series

References in corpus (1)

• On Hecke Eigenvalues at Piatetski-Shapiro Primes