The arithmetic and geometry of Salem numbers (Q2718943)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: The arithmetic and geometry of Salem numbers |
scientific article; zbMATH DE number 1597838
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The arithmetic and geometry of Salem numbers |
scientific article; zbMATH DE number 1597838 |
Statements
The arithmetic and geometry of Salem numbers (English)
0 references
14 May 2001
0 references
Salem number
0 references
arithmetic manifolds
0 references
hyperbolic groups
0 references
Alexander polynomial
0 references
L-function
0 references
Mahler measure
0 references
0 references
This paper is an excellent exposition of certain aspects of the Salem numbers, those real algebraic integers greater than 1, all of whose other conjugates lie within the unit circle with at least one conjugate on the unit circle. One of the more valuable sections of the paper is section 3, which treats the relationship between Salem numbers and the lengths of geodesics on arithmetic hyperbolic surfaces. Other sections consider special classes of Salem numbers arising, e.g. as growth exponents of certain hyperbolic groups or as roots of Alexander polynomials of pretzel knots. There is also a section on Chinburg's construction of Salem numbers from values of L-functions. The paper has 51 references to the literature.
0 references
