no. 1
Number Theory
Empirical estimates of the average orders of orbits period lengths in Euler groups
[Estimations empiriques des ordres moyens des longueurs des périodes d'orbites dans les groupes d'Euler]

Présenté par : Vladimir Arnold

Aicardi, Francesca1
1 Sistiana Mare 56 pr, 34019 Trieste, Italy
Comptes Rendus. Mathématique, Tome 339 (2004) no. 1, pp. 15-20.

On donne une estimation expérimentale du taux moyen de croissance de la longueur de la période des progressions géométriques {q t mod n,t=0,1,...} pour n croissant, pour des valeurs différentes de q. Les résultats empiriques, obtenus pour n jusqu'à 106, permettent de conjecturer que l'ordre moyen de la longueur de la période est Cn ln (n), où la constante C dépend de q.

The averaged growth rate of period's length of the geometrical progressions {q t mod n,t=0,1,...} for increasing n is empirically estimated for different values of q. The experimental results, obtained for n up to 106, allow us to conjecture that the average order of period's length is Cn ln (n), where constant C depends on q.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.02.021
Aicardi, Francesca 1

1 Sistiana Mare 56 pr, 34019 Trieste, Italy 
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Aicardi, Francesca. Empirical estimates of the average orders of orbits period lengths in Euler groups. Comptes Rendus. Mathématique, Tome 339 (2004) no. 1, pp. 15-20. doi : 10.1016/j.crma.2004.02.021. http://www.numdam.org/articles/10.1016/j.crma.2004.02.021/

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