Subspace theorem

In mathematics, the subspace theorem is a result obtained by Wolfgang M. Schmidt (1972). It states that if L₁,...,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

$|L_{1}(x)\cdots L_{n}(x)|<|x|^{-\epsilon }$

lie in a finite number of proper subspaces of Qⁿ.

Schmidt's subspace theorem was generalised in by Schlickewei (1977) to allow more general absolute values.

==A corollary ]].

References

• Schmidt, Wolfgang M. (1972), "Norm form equations", Annals of Mathematics. Second Series, 96: 526–551, ISSN 0003-486X, MR0314761

• Wolfgang M. Schmidt. Diophantine approximation. Lecture Notes in Mathematics 785. Springer. (1980 [1996 with minor corrections])
• Wolfgang M. Schmidt.Diophantine approximations and Diophantine equations, Lecture Notes in Mathematics, Springer Verlag 2000