Almost sure bounds for a weighted Steinhaus random multiplicative function

Abstract

We obtain almost sure bounds for the weighted sum ${\sum }_{n\le t}\frac{f(n)}{\sqrt{n}}$, where $f(n)$ is a Steinhaus random multiplicative function. Specifically, we obtain the bounds predicted by exponentiating the law of the iterated logarithm, giving sharp upper and lower bounds.

22 pages. Comments welcome

References in corpus (2)

• Moments of polynomials with random multiplicative coefficients
• Partial sums of random multiplicative functions and extreme values of a model for the Riemann zeta function

Cited by in corpus (1)

• Moments of random multiplicative functions over function fields