Ruslan Kostohryz

Laws of the iterated logarithm for random Dirichlet series with general weights

For each $s>0$, we consider a random Dirichlet series $X(s)=\sum_{k\geq 1}k^{-1/2-s}a_k\eta_k$, where $\eta_1$, $\eta_2,\ldots$ are independent and identically distributed random variables with mean zero and finite positive variance, and $(a_k)_{k\geq 1}$ is a deterministic sequence of real numbers satisfying $\sum_{k\...