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On the distribution of the order and index of g(mod p) over residue classes II

Pieter Moree
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Abstract

For a fixed rational number g different from -1,0,1 and integers a and d the set N_g(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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Pieter Moree. 2004-04-19. On the distribution of the order and index of g(mod p) over residue classes II. https://doi.org/10.1016/j.jnt.2005.06.006

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