The arithmetic and geometry of Salem numbers

Authors
Ghate, E Hironaka, E
Citation
E. Ghate et E. Hironaka, The arithmetic and geometry of Salem numbers, B AM MATH S, 38(3), 2001, pp. 293-314
Citations number
51
Categorie Soggetti
Mathematics
Journal title
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
02730979 → ACNP
Volume
38
Issue
3
Year of publication
2001
Pages
293 - 314
Database
ISI
SICI code
0273-0979(2001)38:3<293:TAAGOS>2.0.ZU;2-I
Abstract
A Salem number is a real algebraic integer, greater than 1, with the proper ty that all of its conjugates lie on or within the unit circle, and at leas t one conjugate lies on the unit circle. In this paper we survey some of th e recent appearances of Salem numbers in parts of geometry and arithmetic, and discuss the possible implications for the 'minimization problem'. This is an old question in number theory which asks whether the set of Salem num bers is bounded away from 1.