An almost sure upper bound for random multiplicative functions on integers with a large prime factor
نویسندگان
چکیده
Let f be a Rademacher or Steinhaus random multiplicative function. ?>0 small. We prove that, as x?+?, we almost surely have | ? n?xP(n)>xf(n)|? x(loglogx)1?4+?, where P(n) stands for the largest prime factor of n. This gives an indication sure size fluctuations f.
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2022
ISSN: ['1083-6489']
DOI: https://doi.org/10.1214/22-ejp751