On the slopes of the lattice of sections of hermitian line bundles

In this paper we apply Arakelov theory to study the distribution of the Petersson norms of classical cusp forms as well as the distribution of the sup norms of rational functions on adelic subsets of curves. The method in both cases is to study the limiting distribution of the successive minima of norms of global sections of powers of a metrized ample line bundle as one takes increasing powers of the bundle. We develop a general method for computing the measure associated to this distribution. We also study measures associated to the zeros of sections which have small norm.