# A Generalization of the Subspace Theorem With Polynomials of Higher Degree

• Jan-Hendrik Evertse
• Roberto G. Ferretti
Conference paper
Part of the Developments in Mathematics book series (DEVM, volume 16)

## Abstract

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 of ℚ), n a positive integer, 0 < δ 1 and S a finite set of places of K. For v ∈ S, let $$L_0^{\left( v \right)} , \ldots ,L_n^{\left( v \right)}$$ be linearly independent linear forms in [x 0,...,x n ]. Then the set of solutions x ∈ℙn(K) of
$$\log \left( {\prod\limits_{v \in S} {\prod\limits_{i = 0}^n {\frac{{\left| {L_i^{\left( v \right)} \left( x \right)} \right|_v }} {{\left\| x \right\|_v }}} } } \right) \leqslant - \left( {n + 1 + \delta } \right)h\left( x \right)$$
(1.1)
is contained in the union of finitely many proper linear subspaces of ℙn.

## Keywords

Diophantine approximation subspace theorem

11J68 11J25

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