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1.1 The Subspace Theorem can be stated as follows. Let K be a number field (assumed to be contained in some given algebraic closure L0( v ) , ¼,Ln( v )L_0^{\left( v \right)} , \ldots ,L_n^{\left( v \right)} be linearly independent linear forms in log( Õv Î S Õi = 0n \frac| Li( v ) ( x ) |v || x ||v ) \leqslant - ( n + 1 + d )h( x )\log \left( {\prod\limits_{v \in S} {\prod\limits_{i = 0}^n {\frac{{\left| {L_i^{\left( v \right)} \left( x \right)} \right|_v }}{{\left\| x \right\|_v }}} } } \right) \leqslant - \left( {n + 1 + \delta } \right)h\left( x \right) ((1.1)) is contained in the union of finitely many proper linear subspaces of ℙn.

A Generalization of the Subspace Theorem With Polynomials of Higher Degree