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 . 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.
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 [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.
@article{JTNB_1996__8_1_159_0, author = {Manstavi\v{c}ius, Eugenijus}, title = {Natural divisors and the brownian motion}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {159--171}, publisher = {Universit\'e Bordeaux I}, volume = {8}, number = {1}, year = {1996}, mrnumber = {1399952}, zbl = {0864.11040}, language = {en}, url = {http://archive.numdam.org/item/JTNB_1996__8_1_159_0/} }
Manstavičius, Eugenijus. Natural divisors and the brownian motion. Journal de théorie des nombres de Bordeaux, Tome 8 (1996) no. 1, pp. 159-171. http://archive.numdam.org/item/JTNB_1996__8_1_159_0/
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