We prove that any 푞 ‐automatic multiplicative function 푓:ℕ→ℂ either essentially coincides with a Dirichlet character, or vanishes on all sufficiently large primes. This confirms a strong form of a conjecture of Bell, Bruin and Coons [Trans. Amer. Math. Soc. 364 (2012) 933–959].
- 11B85 (primary)
- 68R15 (secondary)