Editing Geometry of numbers (section)

===Subspace theorem of W. M. Schmidt===
{{Main article|Subspace theorem}}
{{See also|Siegel's lemma|volume (mathematics)|determinant|parallelepiped}}
In the geometry of numbers, the [[subspace theorem]] was obtained by [[Wolfgang M. Schmidt]] in 1972.<ref>Schmidt, Wolfgang M. ''Norm form equations.'' Ann. Math. (2) '''96''' (1972), pp. 526–551.

See also Schmidt's books; compare Bombieri and Vaaler and also Bombieri and Gubler.</ref> It states that if ''n'' is a positive integer, and ''L''<sub>1</sub>,...,''L''<sub>''n''</sub> are [[linear independence|linearly independent]] [[linear]] [[algebraic form|forms]] in ''n'' variables with [[algebraic number|algebraic]] coefficients and if ε>0 is any given real number, then the non-zero integer points ''x'' in ''n'' coordinates with
:<math>|L_1(x)\cdots L_n(x)|<|x|^{-\varepsilon}</math>
lie in a finite number of [[linear subspace|proper subspaces]] of '''Q'''<sup>''n''</sup>.