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

Steve Wright

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arXiv · 1304.2191

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

Steve Wright

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Abstract

Let $\mathcal{A}$ denote a finite set of arithmetic progressions of positive integers and let $s \geq 2$ 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 $p$.

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Steve Wright. 2013-04-08. On the density of primes with a set of quadratic residues or non-residues in given arithmetic progression. https://arxiv.org/abs/1304.2191

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