Abstract
Let f be a Rademacher or a Steinhaus random multiplicative function. Let small. We prove that, as , we almost surely have
where stands for the largest prime factor of n. This gives an indication of the almost sure size of the largest fluctuations of f.
Funding Statement
The author is funded by a Departmental Award and by an EPSRC Doctoral Training Partnership Award.
Acknowledgments
The author would like to thank his supervisor Adam J. Harper for guiding him through the work that led to this paper, and the anonymous referee for suggestions that improved its quality.
Citation
Daniele Mastrostefano. "An almost sure upper bound for random multiplicative functions on integers with a large prime factor." Electron. J. Probab. 27 1 - 21, 2022. https://doi.org/10.1214/22-EJP751
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