The necessary and sufficient condition for an algebraic integer to be a Salem number

Abstract

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. We determine the probability of fulfillment the condition for an arbitrary power of the root.

13 pages, 2 figures, 2 tables

References in corpus (2)

• On the number of roots of self-inversive polynomials on the complex unit circle
• On distribution modulo 1 of the sum of powers of a Salem number

Cited by in corpus (1)

• Polynomials with symmetric zeros