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

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

2004-04-19

arxiv.org/abs/math/0404339v1

J. Number Theory 117 (2006), 330-354

Mathematics

Number Theory

18 pages

Scientific paper

10.1016/j.jnt.2005.06.006

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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