Geodesic
On the distribution of the order over residue classes
Moree, Pieter1
1Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111 Bonn, Germany
Electronic research announcements of the American Mathematical Society, Tome 12 (2006), pp. 121-128

Voir la notice de l'article provenant de la source American Mathematical Society

For a fixed rational number $g\not \in \{-1,0,1\}$ and integers $a$ and $d$ we consider the set $N_g(a,d)$ of primes $p$ such that the order of $g$ modulo $p$ is congruent to $a (\textrm {mod~}d)$. Under the Generalized Riemann Hypothesis (GRH), it can be shown that the set $N_g(a,d)$ has a natural density $\delta _g(a,d)$. Arithmetical properties of $\delta _g(a,d)$ are described, and $\delta _g(a,d)$ is compared with $\delta (a,d)$: the average density of elements in a field of prime characteristic having order congruent to $a (\textrm {mod~}d)$. It transpires that $\delta _g(a,d)$ has a strong tendency to be equal to $\delta (a,d)$, or at least to be close to it.
DOI : 10.1090/S1079-6762-06-00168-5

Moree, Pieter  1

1 Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111 Bonn, Germany 
Moree, Pieter. On the distribution of the order over residue classes. Electronic research announcements of the American Mathematical Society, Tome 12 (2006), pp. 121-128. doi: 10.1090/S1079-6762-06-00168-5
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