Asymptotic For Primitive Roots Producing Polynomials

2016/09/02 by Carella, N. A.
#FOS: Mathematics #General Mathematics (math.GM) #Primary 11A07 #Secondary 11N37

paper · doi:10.48550/arxiv.1609.01147

Abstract

Let x ≥ 1 be a large number, let f(x) ∈ ℤ[x] be a prime polynomial of degree deg(f)=m, and let u≠ ± 1, v² be a fixed integer. Assuming the Bateman-Horn conjecture, an asymptotic counting function for the number of primes p=f(n) ≤ x with a fixed primitve root u is derived in this note.

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