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math.NT2023
Pisot numbers, Salem numbers, and generalised polynomials
Jakub Byszewski, Jakub Konieczny
We study sets of integers that can be defined by the vanishing of a generalised polynomial expression. We show that this includes sets of values of linear recurrent sequences of Sa…
math.NT2016
Automatic sequences, generalised polynomials, and nilmanifolds
Jakub Byszewski, Jakub Konieczny
We conjecture that bounded generalised polynomial functions cannot be generated by finite automata, except for the trivial case when they are periodic away from a finite set. Using…