Abstract
There are two very special classes of algebraic integers that arise repeatedly and naturally in this area of study. Recall that an algebraic integer is any root of any monic polynomial with integer coefficients. A real algebraic integer α is a Pisot number if all its conjugate roots have modulus strictly less than 1. A real algebraic integer α is a Salem number if all its conjugate roots have modulus at most 1, and at least one (and hence (see E2) all but one) of the conjugate roots has modulus exactly 1. As is traditional, though somewhat confusing, we denote the class of all Pisot numbers by S and the class of all Salem numbers by T.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Selected References
M.-J. Bertin et al., Pisot and Salem numbers, Birkhäuser, Basel, 1992.
D. Boyd, Variations on a theme of Kronecker, Canad. Math. Bull. 21 (1978), 129–133.
D. Boyd, Pisot and Salem numbers in intervals of the real line, Math. Comp. 32 (1978), 1244–1260.
G. Everest and T. Ward, Heights of Polynomials and Entropy in Algebraic Dynamics, Springer-Verlag, London, 1999.
R. Salem, Algebraic Numbers and Fourier Analysis, D.C. Heath and Co., Boston, MA, 1963.
A. Schinzel, Polynomials with Special Regard to Reducibility, Cambridge University Press, Cambridge, 2000.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Borwein, P. (2002). Pisot and Salem Numbers. In: Computational Excursions in Analysis and Number Theory. CMS Books in Mathematics / Ouvrages de mathématiques de la SMC. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21652-2_3
Download citation
DOI: https://doi.org/10.1007/978-0-387-21652-2_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3000-2
Online ISBN: 978-0-387-21652-2
eBook Packages: Springer Book Archive