On primes in arithmetic progression having a prescribed primitive root. II
نویسنده
چکیده
Let a and f be coprime positive integers. Let g be an integer. Under the Generalized Riemann Hypothesis (GRH) it follows by a result of H.W. Lenstra that the set of primes p such that p ≡ a(mod f) and g is a primitive root modulo p has a natural density. In this note this density is explicitly evaluated with an Euler product as result.
منابع مشابه
On the density of primes in arithmetic progression having a prescribed primitive root
Let g ∈ Q be not −1 or a square. Let Pg denote the set of primes p such that g is a primitive root mod p. Let 1 ≤ a ≤ f, (a, f) = 1. Under the Generalized Riemann Hypothesis (GRH) it can be shown that the set of primes p ∈ Pg with p ≡ a(mod f) has a natural density. In this note this density is explicitly evaluated. This generalizes a classical result of Hooley.
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