A logarithmic structure theorem for multiplicative functions with small partial sums

Dimitris Koukoulopoulos

Let $D\in \mathbb{N}$, let $A>D+1$, and let $Q⩾3$. Consider the class of multiplicative functions $f:\mathbb{N}\to \mathbb{C}$ such that $|\sum_{n\leqslant x}f(n)|\le x(\log…