The height zeta function method for rational points on projective space.

Abstract

We look at n-dimensional rational projective spaces. On these spaces we define a height function and we count the number N(B) of points with height smaller or equal to a bound B. In particular we are interested in the growth rate of N(B) for large B. We give two different methods to solve this problem. We will generalize the second method to specifically chosen subsets of n-dimensional rational projective spaces.