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Abstract
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We show that the derivative of the minimal polynomial of a Salem (resp. Pisot) number
of degree
(resp. ) has
zeros with
modulus less than
and a real zero
satisfying
(resp. ,
except when
belongs to a set of nine explicitly listed elements).
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Keywords
Salem polynomials, Pisot polynomials, Gauss–Lucas theorem,
Cohn's theorem
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Mathematical Subject Classification
Primary: 11R06, 12D10
Secondary: 11C08, 30C15
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Milestones
Received: 10 May 2021
Revised: 18 January 2022
Accepted: 1 February 2022
Published: 15 October 2022
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