Diophantine geometry | Lemmas | Diophantine approximation

Siegel's lemma

In mathematics, specifically in transcendental number theory and Diophantine approximation, Siegel's lemma refers to bounds on the solutions of linear equations obtained by the construction of auxiliary functions. The existence of these polynomials was proven by Axel Thue; Thue's proof used Dirichlet's box principle. Carl Ludwig Siegel published his lemma in 1929. It is a pure existence theorem for a system of linear equations. Siegel's lemma has been refined in recent years to produce sharper bounds on the estimates given by the lemma. (Wikipedia).

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Related pages

Linear equation | Axel Thue | Polynomial | Greatest common divisor | System of linear equations | Diophantine approximation | Transpose | Mathematics | Auxiliary function | Coefficient | Existence theorem | Geometry of numbers | Minor (linear algebra) | Transcendental number theory | Matrix (mathematics) | Pigeonhole principle | Carl Ludwig Siegel