Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
algebraic number
|
| gptkbp:application |
gptkb:geometry
dynamics number theory |
| gptkbp:defines |
A Salem number is a real algebraic integer greater than 1 whose conjugate roots all lie on or within the unit circle, with at least one on the unit circle and at least one outside.
|
| gptkbp:degree |
at least 4
|
| https://www.w3.org/2000/01/rdf-schema#label |
Salem numbers
|
| gptkbp:minimal_polynomial |
reciprocal polynomial
|
| gptkbp:namedAfter |
gptkb:Raphaël_Salem
|
| gptkbp:property |
the minimal polynomial of a Salem number is irreducible over the rationals
every Salem number is a limit point of Pisot numbers every Salem number is a Perron number no Salem number is a Pisot number the set of Salem numbers is countable conjugates on the unit circle come in complex conjugate pairs the set of Salem numbers is closed under taking powers |
| gptkbp:relatedTo |
gptkb:Mahler_measure
Pisot numbers |
| gptkbp:smallestKnownSalemNumber |
Lehmer's number (approximately 1.17628)
|
| gptkbp:studiedBy |
1940s
|
| gptkbp:bfsParent |
gptkb:Raphaël_Salem
|
| gptkbp:bfsLayer |
6
|