Intrinsic Diophantine Approximation on General Polynomial Surfaces
  We study the Hausdorff measure and dimension of the set of intrinsically simultaneously $\psi$-approximable points on a curve, surface, etc., given as a graph of integer valued polynomials. We obtain complete answers to these questions for algebraically "nice" manifolds. This generalizes earlier work done in the case of curves. 
Morten Hein Tiljeset
math.NT