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

Authors
Xi, Ping
Citation
Xi, Ping, Quadratic residues and non-residues for infinitely many Piatetski-Shapiro primes, Acta mathematica Sinica. English series (Print) , 29(3), 2013, pp. 515-522
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
29
Issue
3
Year of publication
2013
Pages
515 - 522
Database
ACNP
SICI code
Abstract
In this paper, we prove a quantitative version of the statement that every nonempty finite subset of .+ 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 Wright in certain aspects.