Integer points on the dilation of a subanalytic surface

Abstract

Let Omega subset ofR(n) be a compact subanalytic set of dimension 2 and tgreater than or equal to1. This paper gives an upper bound as t-->infinity for the number of integer points on the homothetic dilation tOmega of Omega that do not reside on any connected semialgebraic subset of tOmega of positive dimension. Implications for the density of rational points on Omega are also elaborated.