Arakelov invariants of Riemann surfaces

 
R. de Jong

 
 
  We introduce two numerical invariants in Arakelov theory for Riemann surfaces. We show how these invariants can be used to calculate the Arakelov-Green function and the Faltings delta-invariant. We determine their asymptotic behavior and we compute them explicitly for elliptic curves and for Riemann surfaces of genus two.