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arXiv · 2607.22363

Playing with additivity conditions in multiplicative functions

Crystel Bujold·Isabelle Taylor-Daoust
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Abstract

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 $\mathcal{P}_{a,d}=\{a+kd:k\in\mathbb{Z}\}$. Under mild extra conditions on $d$ and $f(a)$, we prove that $f(n)=n\chi(n)$ for all $n$ outside an explicit exceptional set depending on $d$, and some Dirichlet character $\chi$.

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Crystel Bujold, Isabelle Taylor-Daoust. 2026-07-24. Playing with additivity conditions in multiplicative functions. https://arxiv.org/abs/2607.22363

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