On the distribution of the order and index of g (pmod p) over residue classes III

For a fixed rational number g is not an element of (-1, 0, 1) and integers a and d we consider the sets N-g (a, d), respectively R-g (a, d), of primes p for which the order, respectively the index of g (mod p) is congruent to a (mod d). Under the Generalized Riemann Hypothesis (GRH), it is known that these sets have a natural density delta(g)(a, d), respectively rho(g) (a, d). It is shown that these densities can be expressed as linear combinations of certain constants introduced by Pappalardi. Furthermore it is proved that delta(g) (a, d) and rho(g) (a, d) equal their g-averages for almost all g.