The Hausdorff Dimension of Sets of Points Whose Simultaneous Rational Approximation by Sequences of Integer Vectors Have Errors with Small Product Original Research Article

Let m, n, be positive integers and let Q be an infinite subset of imagen. For any number τ, define the set [formula]. It is shown in this paper that if ν set membership, variant [0, n] is the unique number such that the series [formula] is convergent when ε > 0 but divergent when ε < 0, then the Hausdorff dimension of the set EQ(m, n; τ) is dim EQ(m, n; τ) = mn − 1 + (1 + ν)/(1 + τ), for all τ > ν.