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

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

2011-11-11

arxiv.org/abs/1111.2641v2

Mathematics

Number Theory

9 pages, to appear in Acta Math. Sinica, English Series

Scientific paper

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 $1\leqslant c\leqslant243/205$. 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.

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