Computing spaces of effective Arakelov divisors of a number field

The function $h^0$ of a number field is analogous to the dimension of the Riemann-Roch spaces at divisors on an algebraic curve. We provide a method to compute this function for number fields with unit group of rank at most 2, especially in case of large discriminant. This method is based on using LLL-reduced bases and "Jump algorithm" as well as Poisson summation formula.