The Distribution of Primitive Roots

Abstract

Notation,p and q are generic symbols for prime numbers. N(H, p) denotes the number of primes q, not exceeding Hy which are primitive roots (mod p).g(p) denotes the least positive primitive root (mod p).g*(p) is the least prime primitive root (mod p).v(m) denotes the number of distinct prime divisors of the integer m.τk(m) is the number of ways of representing the integer m as the product of k integers, order being important.π(x, k, r) is the number of primes p, not exceeding x, which satisfy p ≡ r(mod k); while π(x) denotes the total number of p ≦ x.logm x denotes the mth iterated logarithmic function which is defined, when possible, by