Abstract
We prove that any q-automatic completely multiplicative function essentially coincides with a Dirichlet character. This answers a question of J.-P. Allouche and L. Goldmakher and confirms a conjecture of J. Bell, N. Bruin and M. Coons for completely multiplicative functions. Further, assuming GRH, the methods allow us to replace completely multiplicative functions with multiplicative functions.
Original language | English |
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Pages (from-to) | 752-755 |
Number of pages | 4 |
Journal | Comptes Rendus Mathematique |
Volume | 357 |
Issue number | 10 |
Early online date | 16 Oct 2019 |
DOIs | |
Publication status | E-pub ahead of print - 16 Oct 2019 |