Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:category |
theorems in number theory
|
| gptkbp:concerns |
gptkb:Diophantine_approximation
|
| gptkbp:field |
number theory
|
| gptkbp:generalizes |
gptkb:Thue's_theorem
gptkb:Siegel's_theorem |
| https://www.w3.org/2000/01/rdf-schema#label |
Thue–Siegel–Roth theorem
|
| gptkbp:implies |
irrational algebraic numbers cannot be approximated too closely by rationals
|
| gptkbp:namedAfter |
gptkb:Klaus_Roth
gptkb:Carl_Ludwig_Siegel gptkb:Axel_Thue |
| gptkbp:provenBy |
gptkb:Klaus_Roth
|
| gptkbp:relatedTo |
gptkb:Liouville's_theorem
transcendental number theory |
| gptkbp:state |
If α is an irrational algebraic number and ε > 0, then there are only finitely many rational numbers p/q such that |α - p/q| < 1/q^{2+ε}.
|
| gptkbp:yearProved |
1955
|
| gptkbp:bfsParent |
gptkb:C._L._Siegel
gptkb:Diophantine_approximation |
| gptkbp:bfsLayer |
6
|