Playing with additivity conditions in multiplicative functions

Crystel Bujold, Isabelle Taylor-Daoust

Let $f:\mathbb{Z}\to \mathbb{C}$ be a multiplicative function. Assume there exist integers $a>1$ and $d>1$ such that $(a,d)=1$ and let ${\mathcal{P}}_{a,d}=\{a+kd:k\in \mathbb{Z}\}$. U…