Computing dimensions of spaces of Arakelov divisors of number fields

Abstract

The function $h^0$ for 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, even with large discriminant. This method is based on using LLL-reduced bases, the "jump algorithm" and Poisson summation formula.

References in corpus (6)

• New upper bounds on sphere packings I
• New upper bounds on sphere packings II
• Computing Arakelov class groups
• On reduced Arakelov divisors of real quadratic fields
• The size function of quadratic extensions of complex quadratic fields
• A generalization of reduced Arakelov divisors of a number field