Singular n-tuples and Hausdorff dimension. II

Abstract

Let n be a natural number, with n ≥ 2. Let Kn denote the set of θ in Euclidean space Rn for which θ1, …, θn, 1 are linearly independent over the rational numbers. We denote points of the set of integer n-tuples Zn by x, y,…. We writeInner product is denoted by θø. In Rl, ‖θ‖ denotes distance to the nearest integer.