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On the distribution of the order over residue classes

Pieter Moree
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Abstract

The multplicative order of an integer g modulo a prime p, with p coprime to g, is defined to be the smallest positive integer k such that g^k is congruent to 1 modulo p. For fixed integers g and d the distribution of this order over residue classes mod d is considered as p runs over the primes. An overview is given of the most significant of my results on this problem obtained (mainly) in the three part series of papers `On the distribution of the order and index of g (modulo p) over residue classes' I-III (appeared in the Journal of Number Theory, also available from the ArXiv).

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Pieter Moree. 2006-08-18. On the distribution of the order over residue classes. https://arxiv.org/abs/math/0608468

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