Oleksiy Klurman, KTH Royal Institute of Technology, Stockholm, SUÈDE, and Max Planck Institut für Math., Bonn, ALLEMAGNE

Classification theorems for multiplicative functions and finite automata

We survey recent developments in multiplicative number theory towards establishing the following fundamental phenomena:
the values of f(n) and f(n+1) are generally independent unless f is of a special form. We illustrate this by describing the proof
of a conjecture by J. Bell, N. Bruin and M. Coons classifying all automatic multiplicative sequences.

The talk is based on a joint work with P. Kurlberg.