On a Turan conjecture and random multiplicative functions

Abstract: We show that if $f$ is the random completely multiplicative function, the probability that $\sum_{n\le x}\frac{f(n)}{n}$ is positive for every $x$ is at least \\ $1-10^{-40}$. For large $x$ we prove an asymptotic upper bound of \\ $O(\exp(-\exp( \frac{\log x}{C\log \log x })))$ on the probability that a particular truncation is negative. This is joint work with Rodrigo Angelo.

number theory

Audience: researchers in the discipline

Combinatorial and additive number theory (CANT 2022)