Let K be a number field, and let W be a subspace of K-N, N >= 1. Let V-1,..., V-M be subspaces of KN of dimension less than dimension of W. We prove the existence of a point of small height in W\boolean OR(M)(i=1) V-i, providing an explicit upper bound on the height of such a point in terms of heights of W and V-1,..., V-M. Our main tool is a counting estimate we prove for the number of points of a subspace of K-N inside of an adelic cube. As corollaries to our main result we derive an explicit bound on the height of a nonvanishing point for a decomposable form and an effective subspace extension lemma.
© 2006 Elsevier
Fukshansky, Lenny. "Siegel's lemma with additional conditions." Journal of Number Theory 120.1 (2006): 13-25.