A note on multiplicative automatic sequences

  title={A note on multiplicative automatic sequences},
  author={Oleksiy Klurman and P. Kurlberg},
  journal={Comptes Rendus Mathematique},
Abstract We prove that any q-automatic completely multiplicative function f : N → C 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. 
A note on multiplicative automatic sequences
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  • Mathematics, Computer Science
  • Adv. Appl. Math.
  • 2017
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