TITLE: Distribution of primitive roots, as p varies
QUESTION [8 upvotes]: For a prime number $p$, let $\Phi(p)$ be the subset of $\{ 1, 2, \ldots, p-1 \}$ consisting of primitive roots modulo $p$.  (Thus $\# \Phi(p) = \phi(p-1)$, where $\phi$ denotes the totient.)  
I am curious about the distribution of $\Phi(p)$ as $p$ varies.  I imagine that this is classic analytic number theory, but I'm finding it surprisingly hard to locate a precise statement/reference.
To make my question precise, consider the following:  For any continuous function $f \colon [0,1] \rightarrow {\mathbb R}$, define
$$D_p(f) = \frac{1}{\phi(p-1)} \cdot \sum_{x \in \Phi(p)} f \left( \frac{x}{p-1} \right).$$
Does this sequence of distributions $D_p$ converge (e.g., weakly in measure, or in some stronger sense?) to the uniform measure or something else on $[0,1]$?  What's the best current result along these lines?

REPLY [3 votes]: A more general result (for general finite fields) is proved in.
Perel’muter, G.I.; Shparlinskij, I.E., The distribution of primitive roots in finite fields, Russ. Math. Surv. 45, No.1, 223-224 (1990); translation from Usp. Mat. Nauk 45, No.1(271), 185-186 (1990). ZBL0705.11078.