On the distribution of the order and index of g(mod p) over residue classes II
Abstract
For a fixed rational number g different from -1,0,1 and integers a and d the set Ng(a,d) of primes p for which the order of g(mod p) is congruent to a(mod d) is considered. It is shown, assuming the Generalized Riemann Hypothesis (GRH), that this set has a natural density which can be computed in terms of degrees of certain Kummer extensions and Galois theoretic intersection coefficients. In case d is a power of an odd prime several properties of this density are established.
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