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- Siegel's_theorem_on_integral_points abstract "In mathematics, Siegel's theorem on integral points is the 1929 result of Carl Ludwig Siegel, that for a smooth algebraic curve C of genus g defined over a number field K, presented in affine space in a given coordinate system, there are only finitely many points on C with coordinates in the ring of integers O of K, provided g > 0. This result covers the Mordell curve, for example.This was proved by combining a version of the Thue–Siegel–Roth theorem, from diophantine approximation, with the Mordell–Weil theorem from diophantine geometry (required in Weil's version, to apply to the Jacobian variety of C). It was the first major result on diophantine equations that depended only on the genus, not any special algebraic form of the equations. For g > 1 it was in the end superseded by Faltings' theorem. Siegel's result was ineffective (see effective results in number theory), since Thue's method in diophantine approximation also is ineffective in describing possible very good rational approximations to algebraic numbers. Effective results in some cases derive from Baker's method.".
- Siegel's_theorem_on_integral_points wikiPageID "3989092".
- Siegel's_theorem_on_integral_points wikiPageRevisionID "502613101".
- Siegel's_theorem_on_integral_points hasPhotoCollection Siegel's_theorem_on_integral_points.
- Siegel's_theorem_on_integral_points subject Category:Diophantine_equations.
- Siegel's_theorem_on_integral_points subject Category:Theorems_in_number_theory.
- Siegel's_theorem_on_integral_points type Abstraction100002137.
- Siegel's_theorem_on_integral_points type Communication100033020.
- Siegel's_theorem_on_integral_points type DiophantineEquations.
- Siegel's_theorem_on_integral_points type Equation106669864.
- Siegel's_theorem_on_integral_points type MathematicalStatement106732169.
- Siegel's_theorem_on_integral_points type Message106598915.
- Siegel's_theorem_on_integral_points type Proposition106750804.
- Siegel's_theorem_on_integral_points type Statement106722453.
- Siegel's_theorem_on_integral_points type Theorem106752293.
- Siegel's_theorem_on_integral_points type TheoremsInNumberTheory.
- Siegel's_theorem_on_integral_points comment "In mathematics, Siegel's theorem on integral points is the 1929 result of Carl Ludwig Siegel, that for a smooth algebraic curve C of genus g defined over a number field K, presented in affine space in a given coordinate system, there are only finitely many points on C with coordinates in the ring of integers O of K, provided g > 0.".
- Siegel's_theorem_on_integral_points label "Siegel's theorem on integral points".
- Siegel's_theorem_on_integral_points sameAs m.0bb8_h.
- Siegel's_theorem_on_integral_points sameAs Q7510553.
- Siegel's_theorem_on_integral_points sameAs Q7510553.
- Siegel's_theorem_on_integral_points sameAs Siegel's_theorem_on_integral_points.
- Siegel's_theorem_on_integral_points wasDerivedFrom Siegel's_theorem_on_integral_points?oldid=502613101.
- Siegel's_theorem_on_integral_points isPrimaryTopicOf Siegel's_theorem_on_integral_points.