On the distribution of primitive roots modulo p

Let p greater than or equal to 3 be a prime. For each primitive root x module p with 1 less than or equal to x less than or equal to p - 1, it is clear that there exists one and only one primitive root (x) over bar module p with 1 less than or equal to (x) over bar less than or equal to p-1 such that x (x) over bar = 1 mod p. Let sigma be a fixed positive number with 0 less than or equal to sigma less than or equal to 1, A denotes the set of all primitive roots module p in interval [1,p]. The main purpose of this paper is to study the asymptotic properties of the mean value [GRAPHICS] ( )and give an interesting asymptotic formula.