Natural divisors and the brownian motion

Manstavičius, Eugenijus

Journal de théorie des nombres de Bordeaux, Volume 8 (1996) no. 1, pp. 159-171.

A model of the Brownian motion defined in terms of the natural divisors is proposed and weak convergence of the related measures in the space $𝐃$ [0,1] is proved. An analogon of the Erdös arcsine law, known for the prime divisors [6] (see [14] for the proof), is obtained. These results together with the author’s investigation [15] extend the systematic study [9] of the distribution of natural divisors. Our approach is based upon the functional limit theorems of probability theory.

On propose un modèle du mouvement brownien relatif aux diviseurs d’un entier, et on établit la convergence faible de la mesure associée dans l’espace $𝐃[0,1]$. On obtient un résultat analogue à celui obtenu par Erdös pour les diviseurs premiers [6] (cf. [14] pour une démonstration). Ces résultats et les recherches de l’auteur [15] étendent l’étude [9] de la distribution des diviseurs. Notre approche s’appuie sur les théorèmes limites fonctionnels en théorie des probabilités.

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