Primitive Root Conjecture in Arithmetic Progressions

2017/01/11 by Carella, N. A.
#11A07 #11N37 #FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.1701.03188

Abstract

Let x≥ 1 be a large number, and let 1 ≤ a 0 constant. This note proves that the counting function for the number of primes p ∈ \p=qn+a: n ≥1 \ with a fixed primitive root u≠ ± 1, v² has the asymptotic formula π_u(x,q,a)=δ(u,q,a)x/ log x +O(x/log^b x), where δ(u,q,a)>0 is the density, and b=b(c)>1 is a constant.

Related

• Simple Proof of the Primitive Root Conjecture
• Uniformly counting primes with a given primitive root and in an\n arithmetic progression
• Asymptotic For Primitive Roots Producing Polynomials
• Small Prime Primitive Roots in Arithmetic Progressions
• Counting primes with a given primitive root, uniformly