On the distribution of the order and index of image over residue classes III Original Research Article

For a fixed rational number gnegated set membership{−1,0,1} and integers a and d we consider the sets Ng(a,d), respectively Rg(a,d), of primes p for which the order, respectively the index of image is congruent to image. Under the Generalized Riemann Hypothesis (GRH), it is known that these sets have a natural density δg(a,d), respectively ρg(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 δg(a,d) and ρg(a,d) equal their g-averages for almost all g.