On the positivity of some weighted partial sums of a random
multiplicative function
On the positivity of some weighted partial sums of a random
multiplicative function
Inspired in the papers by Angelo and Xu, Q.J Math., 74, pp. 767-777, and improvements by Kerr and Klurman, arXiv:2211.05540, we study the probability that the weighted sums of a Rademacher random multiplicative function, $\sum_{n\leq x}f(n)n^{-\sigma}$, are positive for all $x\geq x_\sigma\geq 1$ in the regime $\sigma\to1/2^+$. In a previous …