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

Pieter Moree

Published 2002-11-17, updated 2004-04-19Version 3

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.

Comments: 30 pages, 2 tables. Updated references and some further small changes
Journal: J. Number Theory 114 (2005), 238-271
Categories: math.NT
Subjects: 11N37, 11N69, 11R45
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