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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… Click to show full abstract
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.
Keywords:
automatic sequences;
multiplicative automatic;
multiplicative functions;
completely multiplicative;
note multiplicative
Journal Title: Comptes Rendus Mathematique
Year Published: 2019
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Journal Title: Comptes Rendus Mathematique
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!