The Hausdorff Dimension of Some Exceptional Sets of p-Adic Integer Matrices Original Research Article

J. D. Bovey and M. M. Dodson determined (Acta Arith.45 (1986), 337-358), for each m, n set membership, variant N and real α, the Hausdorff dimension of the set of those linear maps from Zm to the torus Rn/Zn which send infinitely many q=(q1 · · · qm) in Zm to within (max1 ≤ i ≤ m qi)−α of the origin of the torus. In the present paper, we establish an analogous result for sets of linear maps from Zm to Znp.