Almost sure upper bound for random multiplicative functions

2023/04/03 by Caich, Rachid · 2 citations
#FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR)

paper · doi:10.48550/arxiv.2304.00943

Abstract

Let ε >0. Let f be a Steinhaus or Rademacher random multiplicative function. We prove that we have almost surely, as x → +∞, ∑_{n \leqslant x} f(n) ≪ √(x) (log₂ x)^{(3)/(4)+ ε}.

Cited by

• Limit theorems for random Dirichlet series with summation over primes, with an application to Rademacher random multiplicative functions
• A sharp almost sure upper bound for partial sums of random multiplicative functions

Related

• Almost sure bounds for a weighted Steinhaus random multiplicative function
• Almost sure bounds for weighted sums of Rademacher random multiplicative functions
• Bounds for exponential sums with random multiplicative coefficients
• Almost sure large fluctuations of random multiplicative functions
• An almost sure upper bound for random multiplicative functions on integers with a large prime factor