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.
|Number of pages||4|
|Journal||Comptes Rendus Mathematique|
|Early online date||16 Oct 2019|
|Publication status||E-pub ahead of print - 16 Oct 2019|