Natural divisors and the brownian motion
Journal de Théorie des Nombres de Bordeaux, Tome 8 (1996) no. 1, pp. 159-171.

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.

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.

@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},
     doi = {10.5802/jtnb.162},
     zbl = {0864.11040},
     mrnumber = {1399952},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.162/}
}
Eugenijus Manstavičius. Natural divisors and the brownian motion. Journal de Théorie des Nombres de Bordeaux, Tome 8 (1996) no. 1, pp. 159-171. doi : 10.5802/jtnb.162. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.162/

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