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Playing with additivity conditions in multiplicative functions
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.
Versions
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BibTeX
@misc{bujold2026playing,
title = {{Playing with additivity conditions in multiplicative functions}},
author = {Crystel Bujold and Isabelle Taylor-Daoust},
howpublished = {arXiv},
year = {2026},
month = jul,
doi = {10.48550/arxiv.2607.22363},
eprint = {2607.22363},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.22363},
}
RIS
TY - UNPB
TI - Playing with additivity conditions in multiplicative functions
AU - Crystel Bujold
AU - Isabelle Taylor-Daoust
PY - 2026
DA - 2026/07/24
PB - arXiv
DO - 10.48550/arxiv.2607.22363
UR - https://arxiv.org/abs/2607.22363
AB - Let f:ℤ→ℂ be a multiplicative function. Assume there exist integers a>1 and d>1 such that (a,d)=1 and let 𝒫_a,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.
ER -