Abstract

We show that the derivative of the minimal polynomial of a Salem (resp. Pisot) number $\alpha$ of degree $d$ (resp. $d\ge 2$) has $d-2$ zeros with modulus less than $1$ and a real zero $𝜃>1$ satisfying $|𝜃-(d-1)\alpha ∕d|<1∕d$ (resp. $|𝜃-(d-1)\alpha ∕d|<1∕d$, except when $\alpha$ belongs to a set of nine explicitly listed elements).

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