On the density of primes with a set of quadratic residues or non-residues in given arithmetic progression

Abstract

Let $\mathcal{A}$ denote a finite set of arithmetic progressions of positive integers and let $s\ge 2$ be an integer. If the cardinality of $\mathcal{A}$ is at least 2 and $U$ is the union formed by taking certain arithmetic progressions of length $s$ from each element of $\mathcal{A}$, we calculate the asymptotic density of the set of all prime numbers $p$ such that $U$ is a set of quadratic residues (respectively, quadratic non-residues) of $p$.

arXiv comment26 pages, 1 figure. Several improvements to the previous version are made and several errors in that version are corrected. arXiv admin note: text overlap with arXiv:1111.2236

Cited by in corpus (1)

• Quadratic Residues and Non-Residues: Selected Topics