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Playing with additivity conditions in multiplicative functions

2026/07/24 by Crystel Bujold, Isabelle Taylor-Daoust
#math.NT

paper · pdf

Abstract

Let f:ℤ→ℂ be a multiplicative function. Assume there exist integers a>1 and d>1 such that (a,d)=1 and let Pa,d=\a+kd:k∈ℤ\. Under mild extra conditions on d and f(a), we prove that f(n)=nχ(n) for all n outside an explicit exceptional set depending on d, and some Dirichlet character χ.

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