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Title: | A generalized Kubilius-Barban-Vinogradov bound for prime multiplicities |
Authors: | Chen, LHY Jaramillo, A Yang, X |
Issue Date: | 1-Jan-2023 |
Publisher: | ALEA |
Citation: | Chen, L.H.Y., Jaramillo, A. and Yang, X. (2023) 'A generalized Kubilius-Barban-Vinogradov bound for prime multiplicities', Alea (Rio de Janeiro), 20 pp. 713 - 730. doi: 10.30757/ALEA.v20-27. |
Abstract: | We present an assessment of the distance in total variation of arbitrary collections of prime factor multiplicities of a random number in [n] = {1,...,n} and a collection of independent geometric random variables. More precisely, we impose mild conditions on the probability law of the random sample and the aforementioned collection of prime multiplicities, for which a fast decaying bound on the distance towards a tuple of geometric variables holds. Our results generalize and complement those from Kubilius (1964) and Barban and Vinogradov (1964) which consider the particular case of uniform samples in [n] and collection of “small primes”. As applications, we show a generalized version of the celebrated Erdös Kac theorem for not necessarily uniform samples of numbers. |
Description: | Mathematics Subject Classification. 60B12, 11K65. A preprint version of the article is available at arXiv:2111.07361v1 [math.PR], https://arxiv.org/abs/2111.07361v1. It has not been certified by peer review. |
URI: | https://bura.brunel.ac.uk/handle/2438/29291 |
DOI: | https://doi.org/10.30757/ALEA.v20-27 |
Other Identifiers: | ORCiD: Xiaochuan Yang https://orcid.org/0000-0003-2435-4615 60B12 11K65 arXiv:2111.07361v1 [math.PR] |
Appears in Collections: | Dept of Mathematics Research Papers |
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