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An almost sure upper bound for random multiplicative functions on integers with a large prime factor
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Mastrostefano, Daniele (2022) An almost sure upper bound for random multiplicative functions on integers with a large prime factor. Electronic Journal of Probability, 27 . doi:10.1214/22-EJP751 ISSN 1083-6489.
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WRAP-An-almost-sure-upper-bound-for-random-multiplicative-functions-on-integers-with-a-large-prime-factor-Mastrostefano-22.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (567Kb) | Preview |
Official URL: http://dx.doi.org/10.1214/22-EJP751
Abstract
Let f be a Rademacher or a Steinhaus random multiplicative function. Let ε>0 small. We prove that, as x→+∞, we almost surely have
∣∑n≤xP(n)>√x f(n)∣≤√x(loglogx)1∕4+ε,
where P(n) stands for the largest prime factor of n. This gives an indication of the almost sure size of the largest fluctuations of f.
Item Type: | Journal Article | ||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||
Library of Congress Subject Headings (LCSH): | Iterative methods (Mathematics), Random variables , Probabilistic number theory | ||||||||||
Journal or Publication Title: | Electronic Journal of Probability | ||||||||||
Publisher: | University of Washington. Dept. of Mathematics | ||||||||||
ISSN: | 1083-6489 | ||||||||||
Official Date: | 2022 | ||||||||||
Dates: |
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Volume: | 27 | ||||||||||
Number of Pages: | 21 | ||||||||||
DOI: | 10.1214/22-EJP751 | ||||||||||
Status: | Peer Reviewed | ||||||||||
Publication Status: | Published | ||||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||||
Date of first compliant deposit: | 6 June 2022 | ||||||||||
Date of first compliant Open Access: | 7 June 2022 | ||||||||||
RIOXX Funder/Project Grant: |
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