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

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

2002-11-17

arxiv.org/abs/math/0211259v3

J. Number Theory 114 (2005), 238-271

Mathematics

Number Theory

30 pages, 2 tables. Updated references and some further small changes

Scientific paper

10.1016/j.jnt.2004.09.004

For a fixed rational number g, not equal to -1,0 or 1 and integers a and d we consider the set of primes p for which the order of g(mod p) is congruent to a(mod d). For d=4 and d=3 it is shown that, under the Generalized Riemann Hypothesis, these sets have a natural density. Moreover, we explicitly compute this density. For d=4 this generalises earlier work by K. Chinen and L. Murata. The case d=3 was apparently not considered before.

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