A necessary and sufficient condition for an algebraic integer to be a Salem number
Dragan Stankov · Journal de Théorie des Nombres de Bordeaux · 2019
We present a necessary and sufficient condition for a root greater than unity of a monic reciprocal polynomial of an even degree at least four, with integer coefficients, to be a Salem number. This condition requires that the minimal polynomial of some power of the algebraic integer has a linear coefficient that is relatively large. We also determine the probability that an arbitrary power of a Salem number, of certain small degrees, satisfies this condition.