English

Computing dimensions of spaces of Arakelov divisors of number fields

Number Theory 2016-09-12 v2

Abstract

The function h0h^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.

Keywords

Cite

@article{arxiv.1506.04540,
  title  = {Computing dimensions of spaces of Arakelov divisors of number fields},
  author = {Ha Thanh Nguyen Tran},
  journal= {arXiv preprint arXiv:1506.04540},
  year   = {2016}
}