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In mathematics, the subspace theorem is a result obtained by . It states that if ''L''1,...,''L''''n'' are linearly independent linear forms in ''n'' variables with algebraic coefficients and if ε>0 is any given real number, then the non-zero integer points ''x'' with : lie in a finite number of proper subspaces of Q''n''. A quantitative form of the theorem, in which the number of subspaces containing all solutions, was also obtained by Schmidt, and the theorem was generalised by to allow more general absolute values on number fields. The theorem may be used to obtain results on Diophantine equations such as Siegel's theorem on integral points and solution of the S-unit equation. ==A corollary on Diophantine approximation== The following corollary to the subspace theorem is often itself referred to as the ''subspace theorem''. If ''a''1,...,''a''''n'' are algebraic such that 1,''a''1,...,''a''''n'' are linearly independent over Q and ε>0 is any given real number, then there are only finitely many rational ''n''-tuples (''x''1/y,...,''x''''n''/y) with : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「subspace theorem」の詳細全文を読む スポンサード リンク
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